Best Known (110−14, 110, s)-Nets in Base 7
(110−14, 110, 1647090)-Net over F7 — Constructive and digital
Digital (96, 110, 1647090)-net over F7, using
- trace code for nets [i] based on digital (41, 55, 823545)-net over F49, using
- net defined by OOA [i] based on linear OOA(4955, 823545, F49, 14, 14) (dual of [(823545, 14), 11529575, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(4955, 5764815, F49, 14) (dual of [5764815, 5764760, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(10) [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(4941, 5764801, F49, 11) (dual of [5764801, 5764760, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 494−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(492, 14, F49, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,49)), using
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- Reed–Solomon code RS(47,49) [i]
- discarding factors / shortening the dual code based on linear OA(492, 49, F49, 2) (dual of [49, 47, 3]-code or 49-arc in PG(1,49)), using
- construction X applied to Ce(13) ⊂ Ce(10) [i] based on
- OA 7-folding and stacking [i] based on linear OA(4955, 5764815, F49, 14) (dual of [5764815, 5764760, 15]-code), using
- net defined by OOA [i] based on linear OOA(4955, 823545, F49, 14, 14) (dual of [(823545, 14), 11529575, 15]-NRT-code), using
(110−14, 110, large)-Net over F7 — Digital
Digital (96, 110, large)-net over F7, using
- 71 times duplication [i] based on 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
- t-expansion [i] based on digital (94, 109, large)-net over F7, using
(110−14, 110, large)-Net in Base 7 — Upper bound on s
There is no (96, 110, large)-net in base 7, because
- 12 times m-reduction [i] would yield (96, 98, large)-net in base 7, but