Best Known (43, 56, s)-Nets in Base 7
(43, 56, 2801)-Net over F7 — Constructive and digital
Digital (43, 56, 2801)-net over F7, using
- net defined by OOA [i] based on linear OOA(756, 2801, F7, 13, 13) (dual of [(2801, 13), 36357, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 6-folding and stacking with additional row [i] based on linear OA(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using
(43, 56, 13745)-Net over F7 — Digital
Digital (43, 56, 13745)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(756, 13745, F7, 13) (dual of [13745, 13689, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(756, 16807, F7, 13) (dual of [16807, 16751, 14]-code), using
(43, 56, large)-Net in Base 7 — Upper bound on s
There is no (43, 56, large)-net in base 7, because
- 11 times m-reduction [i] would yield (43, 45, large)-net in base 7, but