Best Known (60−25, 60, s)-Nets in Base 8
(60−25, 60, 256)-Net over F8 — Constructive and digital
Digital (35, 60, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 30, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
(60−25, 60, 258)-Net in Base 8 — Constructive
(35, 60, 258)-net in base 8, using
- trace code for nets [i] based on (5, 30, 129)-net in base 64, using
- 5 times m-reduction [i] based on (5, 35, 129)-net in base 64, using
- base change [i] based on digital (0, 30, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 30, 129)-net over F128, using
- 5 times m-reduction [i] based on (5, 35, 129)-net in base 64, using
(60−25, 60, 268)-Net over F8 — Digital
Digital (35, 60, 268)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(860, 268, F8, 25) (dual of [268, 208, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(860, 270, F8, 25) (dual of [270, 210, 26]-code), using
- 9 step Varšamov–Edel lengthening with (ri) = (1, 8 times 0) [i] based on linear OA(859, 260, F8, 25) (dual of [260, 201, 26]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(858, 258, F8, 25) (dual of [258, 200, 26]-code), using
- trace code [i] based on linear OA(6429, 129, F64, 25) (dual of [129, 100, 26]-code), using
- extended algebraic-geometric code AGe(F,103P) [i] based on function field F/F64 with g(F) = 4 and N(F) ≥ 129, using
- trace code [i] based on linear OA(6429, 129, F64, 25) (dual of [129, 100, 26]-code), using
- linear OA(858, 259, F8, 24) (dual of [259, 201, 25]-code), using Gilbert–Varšamov bound and bm = 858 > Vbs−1(k−1) = 11462 278507 738001 212034 466278 914644 073030 475410 087616 [i]
- linear OA(80, 1, F8, 0) (dual of [1, 1, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(80, s, F8, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(858, 258, F8, 25) (dual of [258, 200, 26]-code), using
- construction X with Varšamov bound [i] based on
- 9 step Varšamov–Edel lengthening with (ri) = (1, 8 times 0) [i] based on linear OA(859, 260, F8, 25) (dual of [260, 201, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(860, 270, F8, 25) (dual of [270, 210, 26]-code), using
(60−25, 60, 20811)-Net in Base 8 — Upper bound on s
There is no (35, 60, 20812)-net in base 8, because
- 1 times m-reduction [i] would yield (35, 59, 20812)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 191606 985435 588000 078633 205158 083169 844141 778561 682192 > 859 [i]