Best Known (126, 126+19, s)-Nets in Base 8
(126, 126+19, 932102)-Net over F8 — Constructive and digital
Digital (126, 145, 932102)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 16, 36)-net over F8, using
- 1 times m-reduction [i] based on digital (7, 17, 36)-net over F8, using
- digital (110, 129, 932066)-net over F8, using
- net defined by OOA [i] based on linear OOA(8129, 932066, F8, 19, 19) (dual of [(932066, 19), 17709125, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8129, 8388595, F8, 19) (dual of [8388595, 8388466, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8129, large, F8, 19) (dual of [large, large−129, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8129, large, F8, 19) (dual of [large, large−129, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8129, 8388595, F8, 19) (dual of [8388595, 8388466, 20]-code), using
- net defined by OOA [i] based on linear OOA(8129, 932066, F8, 19, 19) (dual of [(932066, 19), 17709125, 20]-NRT-code), using
- digital (7, 16, 36)-net over F8, using
(126, 126+19, 932104)-Net in Base 8 — Constructive
(126, 145, 932104)-net in base 8, using
- (u, u+v)-construction [i] based on
- (7, 16, 38)-net in base 8, using
- base change [i] based on digital (3, 12, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- base change [i] based on digital (3, 12, 38)-net over F16, using
- digital (110, 129, 932066)-net over F8, using
- net defined by OOA [i] based on linear OOA(8129, 932066, F8, 19, 19) (dual of [(932066, 19), 17709125, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8129, 8388595, F8, 19) (dual of [8388595, 8388466, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(8129, large, F8, 19) (dual of [large, large−129, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(8129, large, F8, 19) (dual of [large, large−129, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(8129, 8388595, F8, 19) (dual of [8388595, 8388466, 20]-code), using
- net defined by OOA [i] based on linear OOA(8129, 932066, F8, 19, 19) (dual of [(932066, 19), 17709125, 20]-NRT-code), using
- (7, 16, 38)-net in base 8, using
(126, 126+19, large)-Net over F8 — Digital
Digital (126, 145, large)-net over F8, using
- t-expansion [i] based on digital (125, 145, large)-net over F8, using
- 1 times m-reduction [i] based on digital (125, 146, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8146, large, F8, 21) (dual of [large, large−146, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(8145, large, F8, 21) (dual of [large, large−145, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- 1 times code embedding in larger space [i] based on linear OA(8145, large, F8, 21) (dual of [large, large−145, 22]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8146, large, F8, 21) (dual of [large, large−146, 22]-code), using
- 1 times m-reduction [i] based on digital (125, 146, large)-net over F8, using
(126, 126+19, large)-Net in Base 8 — Upper bound on s
There is no (126, 145, large)-net in base 8, because
- 17 times m-reduction [i] would yield (126, 128, large)-net in base 8, but