Best Known (94, 94+12, s)-Nets in Base 8
(94, 94+12, 2796395)-Net over F8 — Constructive and digital
Digital (94, 106, 2796395)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (10, 16, 195)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (1, 4, 65)-net over F8, using
- net defined by OOA [i] based on linear OOA(84, 65, F8, 3, 3) (dual of [(65, 3), 191, 4]-NRT-code), using
- digital (6, 12, 130)-net over F8, using
- trace code for nets [i] based on digital (0, 6, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- trace code for nets [i] based on digital (0, 6, 65)-net over F64, using
- digital (1, 4, 65)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (78, 90, 2796200)-net over F8, using
- net defined by OOA [i] based on linear OOA(890, 2796200, F8, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(890, 8388601, F8, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(890, 8388602, F8, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- trace code [i] based on linear OOA(6445, 4194301, F64, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6445, 8388602, F64, 12) (dual of [8388602, 8388557, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- OOA 2-folding [i] based on linear OA(6445, 8388602, F64, 12) (dual of [8388602, 8388557, 13]-code), using
- trace code [i] based on linear OOA(6445, 4194301, F64, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(890, 8388602, F8, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(890, 8388601, F8, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(890, 2796200, F8, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
- digital (10, 16, 195)-net over F8, using
(94, 94+12, 2796714)-Net in Base 8 — Constructive
(94, 106, 2796714)-net in base 8, using
- (u, u+v)-construction [i] based on
- (10, 16, 514)-net in base 8, using
- base change [i] based on digital (6, 12, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 6, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 6, 257)-net over F256, using
- base change [i] based on digital (6, 12, 514)-net over F16, using
- digital (78, 90, 2796200)-net over F8, using
- net defined by OOA [i] based on linear OOA(890, 2796200, F8, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(890, 8388601, F8, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(890, 8388602, F8, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- trace code [i] based on linear OOA(6445, 4194301, F64, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6445, 8388602, F64, 12) (dual of [8388602, 8388557, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(6445, large, F64, 12) (dual of [large, large−45, 13]-code), using
- OOA 2-folding [i] based on linear OA(6445, 8388602, F64, 12) (dual of [8388602, 8388557, 13]-code), using
- trace code [i] based on linear OOA(6445, 4194301, F64, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(890, 8388602, F8, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(890, 8388601, F8, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
- net defined by OOA [i] based on linear OOA(890, 2796200, F8, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
- (10, 16, 514)-net in base 8, using
(94, 94+12, large)-Net over F8 — Digital
Digital (94, 106, large)-net over F8, using
- 81 times duplication [i] based on digital (93, 105, large)-net over F8, using
- t-expansion [i] based on digital (90, 105, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8105, large, F8, 15) (dual of [large, large−105, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8105, large, F8, 15) (dual of [large, large−105, 16]-code), using
- t-expansion [i] based on digital (90, 105, large)-net over F8, using
(94, 94+12, large)-Net in Base 8 — Upper bound on s
There is no (94, 106, large)-net in base 8, because
- 10 times m-reduction [i] would yield (94, 96, large)-net in base 8, but