Space them out through the bed you have prepared for them later in the season each will set a few "daughter" plants you can use for rotating plants ever few years. It is easiest to leave the extra room for them from the start so you keep a steady production year to year instead of starting over ever few years. After a plant has been in place for ~3 years, remove it after it has fruited, amend the soil heavily in the "hole", and fill the space with one of the new suckers to keep production up. Once a daughter plant is well rooted, you can cut the connection to its "mother" if you need to move it. I have put the suckers into pots made of old yogurt cups before they started rooting to make transplanting easier when the time came.

I think 4 per square would work, if a but crowded. The runners would fill in any space left over anyway, no matter what your spacing is. Are you planting everbearing, june bearing, or day-neutral? Day neutrals don't need to be renovated, but the other types will need to be replaced every 3-5 years.

I built strawberry pyramids in a 4x4 box. They are three levels to it. The bottom level has a total of 12 strawberry plants (that is basically one foot apart). The second level is about 3x3 in size and I fit about 9 - 10 in there - not quite a foot apart. In the top part, it is only about 8 inches square and only one strawberry is in there.

So by making the pyramids, I am able to fit about 24 strawberry plants in the area. They did very well last year (first year for planting) and expect them to be better this year since they are well-rooted.

When the runners (or daughter plants) are made, I've been mostly throwing them out. But, after next year, I will use the daughter plants to replace all of the other ones (again, a three year rotation as previously mentioned).

Here is a link that might be useful: BsnTech Gardening Blog

I am about to build 4 x 4 boxes for my strawberries, a box for each separate variety. I have 20 plants so most will have 1 per square.

bsntech, those boxes look so neat. Thanks for the link. tishtoshnm, I just bought 15 from lowes, cant remember the type offhand. I am planning a potager so thats where mine will go.
Thanks ray, and homertherat for the great info.
Tammy