Best Known (80, 96, s)-Nets in Base 7
(80, 96, 102946)-Net over F7 — Constructive and digital
Digital (80, 96, 102946)-net over F7, using
- net defined by OOA [i] based on linear OOA(796, 102946, F7, 16, 16) (dual of [(102946, 16), 1647040, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(796, 823568, F7, 16) (dual of [823568, 823472, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(792, 823543, F7, 16) (dual of [823543, 823451, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(771, 823543, F7, 12) (dual of [823543, 823472, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(74, 25, F7, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,7)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- OA 8-folding and stacking [i] based on linear OA(796, 823568, F7, 16) (dual of [823568, 823472, 17]-code), using
(80, 96, 546882)-Net over F7 — Digital
Digital (80, 96, 546882)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(796, 546882, F7, 16) (dual of [546882, 546786, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(796, 823568, F7, 16) (dual of [823568, 823472, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(792, 823543, F7, 16) (dual of [823543, 823451, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(771, 823543, F7, 12) (dual of [823543, 823472, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 823542 = 77−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(74, 25, F7, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,7)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(796, 823568, F7, 16) (dual of [823568, 823472, 17]-code), using
(80, 96, large)-Net in Base 7 — Upper bound on s
There is no (80, 96, large)-net in base 7, because
- 14 times m-reduction [i] would yield (80, 82, large)-net in base 7, but