Best Known (51, 73, s)-Nets in Base 7
(51, 73, 218)-Net over F7 — Constructive and digital
Digital (51, 73, 218)-net over F7, using
- net defined by OOA [i] based on linear OOA(773, 218, F7, 22, 22) (dual of [(218, 22), 4723, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(773, 2398, F7, 22) (dual of [2398, 2325, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(773, 2401, F7, 22) (dual of [2401, 2328, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(773, 2401, F7, 22) (dual of [2401, 2328, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(773, 2398, F7, 22) (dual of [2398, 2325, 23]-code), using
(51, 73, 1514)-Net over F7 — Digital
Digital (51, 73, 1514)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(773, 1514, F7, 22) (dual of [1514, 1441, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(773, 2401, F7, 22) (dual of [2401, 2328, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2400 = 74−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(773, 2401, F7, 22) (dual of [2401, 2328, 23]-code), using
(51, 73, 332071)-Net in Base 7 — Upper bound on s
There is no (51, 73, 332072)-net in base 7, because
- the generalized Rao bound for nets shows that 7m ≥ 49 222217 612042 071282 135981 738864 031346 598541 358826 567860 260353 > 773 [i]