Best Known (68, 78, s)-Nets in Base 9
(68, 78, 3355440)-Net over F9 — Constructive and digital
Digital (68, 78, 3355440)-net over F9, using
- 94 times duplication [i] based on digital (64, 74, 3355440)-net over F9, using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F81, using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 814−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(8137, large, F81, 10) (dual of [large, large−37, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(8137, 8388600, F81, 10) (dual of [8388600, 8388563, 11]-code), using
- net defined by OOA [i] based on linear OOA(8137, 1677720, F81, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F81, using
(68, 78, large)-Net over F9 — Digital
Digital (68, 78, large)-net over F9, using
- 95 times duplication [i] based on digital (63, 73, large)-net over F9, using
- t-expansion [i] based on digital (62, 73, large)-net over F9, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(973, large, F9, 11) (dual of [large, large−73, 12]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 21523360 | 98−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(973, large, F9, 11) (dual of [large, large−73, 12]-code), using
- t-expansion [i] based on digital (62, 73, large)-net over F9, using
(68, 78, large)-Net in Base 9 — Upper bound on s
There is no (68, 78, large)-net in base 9, because
- 8 times m-reduction [i] would yield (68, 70, large)-net in base 9, but