Best Known (143, 143+19, s)-Nets in Base 8
(143, 143+19, 1864169)-Net over F8 — Constructive and digital
Digital (143, 162, 1864169)-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 (127, 146, 1864133)-net over F8, using
- net defined by OOA [i] based on linear OOA(8146, 1864133, F8, 21, 19) (dual of [(1864133, 21), 39146647, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8146, 5592400, F8, 3, 19) (dual of [(5592400, 3), 16777054, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8146, 5592402, F8, 3, 19) (dual of [(5592402, 3), 16777060, 20]-NRT-code), using
- trace code [i] based on linear OOA(6473, 2796201, F64, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6473, large, F64, 19) (dual of [large, large−73, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6473, large, F64, 19) (dual of [large, large−73, 20]-code), using
- trace code [i] based on linear OOA(6473, 2796201, F64, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8146, 5592402, F8, 3, 19) (dual of [(5592402, 3), 16777060, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8146, 5592400, F8, 3, 19) (dual of [(5592400, 3), 16777054, 20]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8146, 1864133, F8, 21, 19) (dual of [(1864133, 21), 39146647, 20]-NRT-code), using
- digital (7, 16, 36)-net over F8, using
(143, 143+19, 1864171)-Net in Base 8 — Constructive
(143, 162, 1864171)-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 (127, 146, 1864133)-net over F8, using
- net defined by OOA [i] based on linear OOA(8146, 1864133, F8, 21, 19) (dual of [(1864133, 21), 39146647, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8146, 5592400, F8, 3, 19) (dual of [(5592400, 3), 16777054, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8146, 5592402, F8, 3, 19) (dual of [(5592402, 3), 16777060, 20]-NRT-code), using
- trace code [i] based on linear OOA(6473, 2796201, F64, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(6473, large, F64, 19) (dual of [large, large−73, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(6473, large, F64, 19) (dual of [large, large−73, 20]-code), using
- trace code [i] based on linear OOA(6473, 2796201, F64, 3, 19) (dual of [(2796201, 3), 8388530, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8146, 5592402, F8, 3, 19) (dual of [(5592402, 3), 16777060, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(8146, 5592400, F8, 3, 19) (dual of [(5592400, 3), 16777054, 20]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8146, 1864133, F8, 21, 19) (dual of [(1864133, 21), 39146647, 20]-NRT-code), using
- (7, 16, 38)-net in base 8, using
(143, 143+19, large)-Net over F8 — Digital
Digital (143, 162, large)-net over F8, using
- 81 times duplication [i] based on digital (142, 161, large)-net over F8, using
- t-expansion [i] based on digital (138, 161, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8161, large, F8, 23) (dual of [large, large−161, 24]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 816−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8161, large, F8, 23) (dual of [large, large−161, 24]-code), using
- t-expansion [i] based on digital (138, 161, large)-net over F8, using
(143, 143+19, large)-Net in Base 8 — Upper bound on s
There is no (143, 162, large)-net in base 8, because
- 17 times m-reduction [i] would yield (143, 145, large)-net in base 8, but