Best Known (78, 78+19, s)-Nets in Base 7
(78, 78+19, 13072)-Net over F7 — Constructive and digital
Digital (78, 97, 13072)-net over F7, using
- net defined by OOA [i] based on linear OOA(797, 13072, F7, 19, 19) (dual of [(13072, 19), 248271, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(797, 117649, F7, 19) (dual of [117649, 117552, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(797, 117649, F7, 19) (dual of [117649, 117552, 20]-code), using
(78, 78+19, 70803)-Net over F7 — Digital
Digital (78, 97, 70803)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(797, 70803, F7, 19) (dual of [70803, 70706, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(797, 117649, F7, 19) (dual of [117649, 117552, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(797, 117649, F7, 19) (dual of [117649, 117552, 20]-code), using
(78, 78+19, large)-Net in Base 7 — Upper bound on s
There is no (78, 97, large)-net in base 7, because
- 17 times m-reduction [i] would yield (78, 80, large)-net in base 7, but