Best Known (95, 105, s)-Nets in Base 7
(95, 105, 3356616)-Net over F7 — Constructive and digital
Digital (95, 105, 3356616)-net over F7, using
- (u, u+v)-construction [i] based on
- digital (8, 13, 1176)-net over F7, using
- net defined by OOA [i] based on linear OOA(713, 1176, F7, 5, 5) (dual of [(1176, 5), 5867, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(713, 2353, F7, 5) (dual of [2353, 2340, 6]-code), using
- net defined by OOA [i] based on linear OOA(713, 1176, F7, 5, 5) (dual of [(1176, 5), 5867, 6]-NRT-code), using
- 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
- digital (8, 13, 1176)-net over F7, using
(95, 105, large)-Net over F7 — Digital
Digital (95, 105, large)-net over F7, using
- t-expansion [i] based on digital (94, 105, large)-net over F7, using
- 4 times m-reduction [i] based on digital (94, 109, large)-net over F7, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(7109, large, F7, 15) (dual of [large, large−109, 16]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 20176804 | 718−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(7109, large, F7, 15) (dual of [large, large−109, 16]-code), using
- 4 times m-reduction [i] based on digital (94, 109, large)-net over F7, using
(95, 105, large)-Net in Base 7 — Upper bound on s
There is no (95, 105, large)-net in base 7, because
- 8 times m-reduction [i] would yield (95, 97, large)-net in base 7, but