Best Known (94−19, 94, s)-Nets in Base 7
(94−19, 94, 1883)-Net over F7 — Constructive and digital
Digital (75, 94, 1883)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (4, 13, 16)-net over F7, using
- 3 times m-reduction [i] based on digital (4, 16, 16)-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
- digital (4, 13, 16)-net over F7, using
(94−19, 94, 32613)-Net over F7 — Digital
Digital (75, 94, 32613)-net over F7, using
(94−19, 94, large)-Net in Base 7 — Upper bound on s
There is no (75, 94, large)-net in base 7, because
- 17 times m-reduction [i] would yield (75, 77, large)-net in base 7, but