Best Known (77, 77+19, s)-Nets in Base 7
(77, 77+19, 1895)-Net over F7 — Constructive and digital
Digital (77, 96, 1895)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (6, 15, 28)-net over F7, using
- digital (62, 81, 1867)-net over F7, using
- net defined by OOA [i] based on linear OOA(781, 1867, F7, 19, 19) (dual of [(1867, 19), 35392, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(781, 16804, F7, 19) (dual of [16804, 16723, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(781, 16807, F7, 19) (dual of [16807, 16726, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(781, 16807, F7, 19) (dual of [16807, 16726, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(781, 16804, F7, 19) (dual of [16804, 16723, 20]-code), using
- net defined by OOA [i] based on linear OOA(781, 1867, F7, 19, 19) (dual of [(1867, 19), 35392, 20]-NRT-code), using
(77, 77+19, 40482)-Net over F7 — Digital
Digital (77, 96, 40482)-net over F7, using
(77, 77+19, large)-Net in Base 7 — Upper bound on s
There is no (77, 96, large)-net in base 7, because
- 17 times m-reduction [i] would yield (77, 79, large)-net in base 7, but