Best Known (95, 109, s)-Nets in Base 7
(95, 109, 1647088)-Net over F7 — Constructive and digital
Digital (95, 109, 1647088)-net over F7, using
- 71 times duplication [i] based on digital (94, 108, 1647088)-net over F7, using
- trace code for nets [i] based on digital (40, 54, 823544)-net over F49, using
- net defined by OOA [i] based on linear OOA(4954, 823544, F49, 14, 14) (dual of [(823544, 14), 11529562, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(4954, 5764808, F49, 14) (dual of [5764808, 5764754, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(4954, 5764810, F49, 14) (dual of [5764810, 5764756, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(4953, 5764801, F49, 14) (dual of [5764801, 5764748, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- 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]
- linear OA(491, 9, F49, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(491, s, F49, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(4954, 5764810, F49, 14) (dual of [5764810, 5764756, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(4954, 5764808, F49, 14) (dual of [5764808, 5764754, 15]-code), using
- net defined by OOA [i] based on linear OOA(4954, 823544, F49, 14, 14) (dual of [(823544, 14), 11529562, 15]-NRT-code), using
- trace code for nets [i] based on digital (40, 54, 823544)-net over F49, using
(95, 109, large)-Net over F7 — Digital
Digital (95, 109, large)-net over F7, using
- t-expansion [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
(95, 109, large)-Net in Base 7 — Upper bound on s
There is no (95, 109, large)-net in base 7, because
- 12 times m-reduction [i] would yield (95, 97, large)-net in base 7, but