Best Known (27, 27+18, s)-Nets in Base 8
(27, 27+18, 208)-Net over F8 — Constructive and digital
Digital (27, 45, 208)-net over F8, using
- 3 times m-reduction [i] based on digital (27, 48, 208)-net over F8, using
- trace code for nets [i] based on digital (3, 24, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- trace code for nets [i] based on digital (3, 24, 104)-net over F64, using
(27, 27+18, 258)-Net in Base 8 — Constructive
(27, 45, 258)-net in base 8, using
- 1 times m-reduction [i] based on (27, 46, 258)-net in base 8, using
- trace code for nets [i] based on (4, 23, 129)-net in base 64, using
- 5 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
- base change [i] based on digital (0, 24, 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, 24, 129)-net over F128, using
- 5 times m-reduction [i] based on (4, 28, 129)-net in base 64, using
- trace code for nets [i] based on (4, 23, 129)-net in base 64, using
(27, 27+18, 269)-Net over F8 — Digital
Digital (27, 45, 269)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(845, 269, F8, 18) (dual of [269, 224, 19]-code), using
- 10 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0) [i] based on linear OA(844, 258, F8, 18) (dual of [258, 214, 19]-code), using
- trace code [i] based on linear OA(6422, 129, F64, 18) (dual of [129, 107, 19]-code), using
- extended algebraic-geometric code AGe(F,110P) [i] based on function field F/F64 with g(F) = 4 and N(F) ≥ 129, using
- trace code [i] based on linear OA(6422, 129, F64, 18) (dual of [129, 107, 19]-code), using
- 10 step Varšamov–Edel lengthening with (ri) = (1, 9 times 0) [i] based on linear OA(844, 258, F8, 18) (dual of [258, 214, 19]-code), using
(27, 27+18, 19408)-Net in Base 8 — Upper bound on s
There is no (27, 45, 19409)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 43572 450199 862111 883255 829999 791570 634240 > 845 [i]