Best Known (55−22, 55, s)-Nets in Base 8
(55−22, 55, 256)-Net over F8 — Constructive and digital
Digital (33, 55, 256)-net over F8, using
- 1 times m-reduction [i] based on digital (33, 56, 256)-net over F8, using
- trace code for nets [i] based on digital (5, 28, 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, 28, 128)-net over F64, using
(55−22, 55, 299)-Net over F8 — Digital
Digital (33, 55, 299)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(855, 299, F8, 22) (dual of [299, 244, 23]-code), using
- 38 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 1, 11 times 0, 1, 22 times 0) [i] based on linear OA(852, 258, F8, 22) (dual of [258, 206, 23]-code), using
- trace code [i] based on linear OA(6426, 129, F64, 22) (dual of [129, 103, 23]-code), using
- extended algebraic-geometric code AGe(F,106P) [i] based on function field F/F64 with g(F) = 4 and N(F) ≥ 129, using
- trace code [i] based on linear OA(6426, 129, F64, 22) (dual of [129, 103, 23]-code), using
- 38 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 1, 11 times 0, 1, 22 times 0) [i] based on linear OA(852, 258, F8, 22) (dual of [258, 206, 23]-code), using
(55−22, 55, 300)-Net in Base 8 — Constructive
(33, 55, 300)-net in base 8, using
- 1 times m-reduction [i] based on (33, 56, 300)-net in base 8, using
- trace code for nets [i] based on (5, 28, 150)-net in base 64, using
- base change [i] based on digital (1, 24, 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, 24, 150)-net over F128, using
- trace code for nets [i] based on (5, 28, 150)-net in base 64, using
(55−22, 55, 22974)-Net in Base 8 — Upper bound on s
There is no (33, 55, 22975)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 46 784234 920250 715415 809201 936616 309766 925389 446996 > 855 [i]