Best Known (59−12, 59, s)-Nets in Base 7
(59−12, 59, 2816)-Net over F7 — Constructive and digital
Digital (47, 59, 2816)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 13)-net over F7, using
- 6 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
- digital (40, 52, 2803)-net over F7, using
- net defined by OOA [i] based on linear OOA(752, 2803, F7, 12, 12) (dual of [(2803, 12), 33584, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(752, 16818, F7, 12) (dual of [16818, 16766, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- linear OA(751, 16807, F7, 12) (dual of [16807, 16756, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(741, 16807, F7, 10) (dual of [16807, 16766, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 16806 = 75−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(71, 11, F7, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(71, s, F7, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(11) ⊂ Ce(9) [i] based on
- OA 6-folding and stacking [i] based on linear OA(752, 16818, F7, 12) (dual of [16818, 16766, 13]-code), using
- net defined by OOA [i] based on linear OOA(752, 2803, F7, 12, 12) (dual of [(2803, 12), 33584, 13]-NRT-code), using
- digital (1, 7, 13)-net over F7, using
(59−12, 59, 27909)-Net over F7 — Digital
Digital (47, 59, 27909)-net over F7, using
(59−12, 59, large)-Net in Base 7 — Upper bound on s
There is no (47, 59, large)-net in base 7, because
- 10 times m-reduction [i] would yield (47, 49, large)-net in base 7, but