Best Known (167−20, 167, s)-Nets in Base 8
(167−20, 167, 1677744)-Net over F8 — Constructive and digital
Digital (147, 167, 1677744)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (3, 13, 24)-net over F8, using
- net from sequence [i] based on digital (3, 23)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- the Klein quartic over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 3 and N(F) ≥ 24, using
- net from sequence [i] based on digital (3, 23)-sequence 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
- digital (3, 13, 24)-net over F8, using
(167−20, 167, large)-Net over F8 — Digital
Digital (147, 167, large)-net over F8, using
- t-expansion [i] based on digital (144, 167, large)-net over F8, using
- 1 times m-reduction [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
- 1 times m-reduction [i] based on digital (144, 168, large)-net over F8, using
(167−20, 167, large)-Net in Base 8 — Upper bound on s
There is no (147, 167, large)-net in base 8, because
- 18 times m-reduction [i] would yield (147, 149, large)-net in base 8, but