Best Known (39, 65, s)-Nets in Base 8
(39, 65, 256)-Net over F8 — Constructive and digital
Digital (39, 65, 256)-net over F8, using
- 3 times m-reduction [i] based on digital (39, 68, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 34, 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, 34, 128)-net over F64, using
(39, 65, 300)-Net in Base 8 — Constructive
(39, 65, 300)-net in base 8, using
- 1 times m-reduction [i] based on (39, 66, 300)-net in base 8, using
- trace code for nets [i] based on (6, 33, 150)-net in base 64, using
- 2 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- base change [i] based on digital (1, 30, 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, 30, 150)-net over F128, using
- 2 times m-reduction [i] based on (6, 35, 150)-net in base 64, using
- trace code for nets [i] based on (6, 33, 150)-net in base 64, using
(39, 65, 339)-Net over F8 — Digital
Digital (39, 65, 339)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(865, 339, F8, 26) (dual of [339, 274, 27]-code), using
- 16 step Varšamov–Edel lengthening with (ri) = (1, 15 times 0) [i] based on linear OA(864, 322, F8, 26) (dual of [322, 258, 27]-code), using
- trace code [i] based on linear OA(6432, 161, F64, 26) (dual of [161, 129, 27]-code), using
- extended algebraic-geometric code AGe(F,134P) [i] based on function field F/F64 with g(F) = 6 and N(F) ≥ 161, using
- trace code [i] based on linear OA(6432, 161, F64, 26) (dual of [161, 129, 27]-code), using
- 16 step Varšamov–Edel lengthening with (ri) = (1, 15 times 0) [i] based on linear OA(864, 322, F8, 26) (dual of [322, 258, 27]-code), using
(39, 65, 26523)-Net in Base 8 — Upper bound on s
There is no (39, 65, 26524)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 50231 193661 224910 991389 688941 771411 564156 988862 362166 719460 > 865 [i]