Best Known (27, 43, s)-Nets in Base 8
(27, 43, 256)-Net over F8 — Constructive and digital
Digital (27, 43, 256)-net over F8, using
- 1 times m-reduction [i] based on digital (27, 44, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 22, 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
- trace code for nets [i] based on digital (5, 22, 128)-net over F64, using
(27, 43, 300)-Net in Base 8 — Constructive
(27, 43, 300)-net in base 8, using
- 81 times duplication [i] based on (26, 42, 300)-net in base 8, using
- t-expansion [i] based on (25, 42, 300)-net in base 8, using
- trace code for nets [i] based on (4, 21, 150)-net in base 64, using
- base change [i] based on digital (1, 18, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 18, 150)-net over F128, using
- trace code for nets [i] based on (4, 21, 150)-net in base 64, using
- t-expansion [i] based on (25, 42, 300)-net in base 8, using
(27, 43, 435)-Net over F8 — Digital
Digital (27, 43, 435)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(843, 435, F8, 16) (dual of [435, 392, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(843, 511, F8, 16) (dual of [511, 468, 17]-code), using
(27, 43, 38428)-Net in Base 8 — Upper bound on s
There is no (27, 43, 38429)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 680 700674 667411 621956 249988 333503 282825 > 843 [i]