Best Known (172−20, 172, s)-Nets in Base 8
(172−20, 172, 1677756)-Net over F8 — Constructive and digital
Digital (152, 172, 1677756)-net over F8, using
- 81 times duplication [i] based on digital (151, 171, 1677756)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (7, 17, 36)-net over F8, using
- digital (134, 154, 1677720)-net over F8, using
- net defined by OOA [i] based on linear OOA(8154, 1677720, F8, 22, 20) (dual of [(1677720, 22), 36909686, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(8154, 8388601, F8, 2, 20) (dual of [(8388601, 2), 16777048, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8154, 8388602, F8, 2, 20) (dual of [(8388602, 2), 16777050, 21]-NRT-code), using
- trace code [i] based on linear OOA(6477, 4194301, F64, 2, 20) (dual of [(4194301, 2), 8388525, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(6477, 8388602, F64, 20) (dual of [8388602, 8388525, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(6477, large, F64, 20) (dual of [large, large−77, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(6477, large, F64, 20) (dual of [large, large−77, 21]-code), using
- OOA 2-folding [i] based on linear OA(6477, 8388602, F64, 20) (dual of [8388602, 8388525, 21]-code), using
- trace code [i] based on linear OOA(6477, 4194301, F64, 2, 20) (dual of [(4194301, 2), 8388525, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(8154, 8388602, F8, 2, 20) (dual of [(8388602, 2), 16777050, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(8154, 8388601, F8, 2, 20) (dual of [(8388601, 2), 16777048, 21]-NRT-code), using
- net defined by OOA [i] based on linear OOA(8154, 1677720, F8, 22, 20) (dual of [(1677720, 22), 36909686, 21]-NRT-code), using
- (u, u+v)-construction [i] based on
(172−20, 172, 1677758)-Net in Base 8 — Constructive
(152, 172, 1677758)-net in base 8, using
- base change [i] based on digital (109, 129, 1677758)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 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
- digital (96, 116, 1677720)-net over F16, using
- net defined by OOA [i] based on linear OOA(16116, 1677720, F16, 22, 20) (dual of [(1677720, 22), 36909724, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(16116, 8388601, F16, 2, 20) (dual of [(8388601, 2), 16777086, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16116, 8388602, F16, 2, 20) (dual of [(8388602, 2), 16777088, 21]-NRT-code), using
- trace code [i] based on linear OOA(25658, 4194301, F256, 2, 20) (dual of [(4194301, 2), 8388544, 21]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25658, 8388602, F256, 20) (dual of [8388602, 8388544, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,19], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(25658, large, F256, 20) (dual of [large, large−58, 21]-code), using
- OOA 2-folding [i] based on linear OA(25658, 8388602, F256, 20) (dual of [8388602, 8388544, 21]-code), using
- trace code [i] based on linear OOA(25658, 4194301, F256, 2, 20) (dual of [(4194301, 2), 8388544, 21]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(16116, 8388602, F16, 2, 20) (dual of [(8388602, 2), 16777088, 21]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OOA(16116, 8388601, F16, 2, 20) (dual of [(8388601, 2), 16777086, 21]-NRT-code), using
- net defined by OOA [i] based on linear OOA(16116, 1677720, F16, 22, 20) (dual of [(1677720, 22), 36909724, 21]-NRT-code), using
- digital (3, 13, 38)-net over F16, using
- (u, u+v)-construction [i] based on
(172−20, 172, large)-Net over F8 — Digital
Digital (152, 172, large)-net over F8, using
- 84 times duplication [i] based on digital (148, 168, large)-net over F8, using
- t-expansion [i] based on digital (144, 168, large)-net over F8, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8168, large, F8, 24) (dual of [large, large−168, 25]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 88−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(8168, large, F8, 24) (dual of [large, large−168, 25]-code), using
- t-expansion [i] based on digital (144, 168, large)-net over F8, using
(172−20, 172, large)-Net in Base 8 — Upper bound on s
There is no (152, 172, large)-net in base 8, because
- 18 times m-reduction [i] would yield (152, 154, large)-net in base 8, but