Best Known (94−10, 94, s)-Nets in Base 7
(94−10, 94, 3355440)-Net over F7 — Constructive and digital
Digital (84, 94, 3355440)-net over F7, using
- 72 times duplication [i] based on digital (82, 92, 3355440)-net over F7, using
- trace code for nets [i] based on digital (36, 46, 1677720)-net over F49, using
- net defined by OOA [i] based on linear OOA(4946, 1677720, F49, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(4946, 8388600, F49, 10) (dual of [8388600, 8388554, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(4946, large, F49, 10) (dual of [large, large−46, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 25679568 | 495−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(4946, large, F49, 10) (dual of [large, large−46, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(4946, 8388600, F49, 10) (dual of [8388600, 8388554, 11]-code), using
- net defined by OOA [i] based on linear OOA(4946, 1677720, F49, 10, 10) (dual of [(1677720, 10), 16777154, 11]-NRT-code), using
- trace code for nets [i] based on digital (36, 46, 1677720)-net over F49, using
(94−10, 94, large)-Net over F7 — Digital
Digital (84, 94, large)-net over F7, using
- 74 times duplication [i] based on digital (80, 90, large)-net over F7, using
- t-expansion [i] based on digital (78, 90, large)-net over F7, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(790, large, F7, 12) (dual of [large, large−90, 13]-code), using
- trace code [i] based on linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using
- an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- trace code [i] based on linear OA(4945, 5764801, F49, 12) (dual of [5764801, 5764756, 13]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(790, large, F7, 12) (dual of [large, large−90, 13]-code), using
- t-expansion [i] based on digital (78, 90, large)-net over F7, using
(94−10, 94, large)-Net in Base 7 — Upper bound on s
There is no (84, 94, large)-net in base 7, because
- 8 times m-reduction [i] would yield (84, 86, large)-net in base 7, but