Best Known (95, 127, s)-Nets in Base 4
(95, 127, 531)-Net over F4 — Constructive and digital
Digital (95, 127, 531)-net over F4, using
- 5 times m-reduction [i] based on digital (95, 132, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 44, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 44, 177)-net over F64, using
(95, 127, 576)-Net in Base 4 — Constructive
(95, 127, 576)-net in base 4, using
- 41 times duplication [i] based on (94, 126, 576)-net in base 4, using
- t-expansion [i] based on (93, 126, 576)-net in base 4, using
- trace code for nets [i] based on (9, 42, 192)-net in base 64, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 36, 192)-net over F128, using
- trace code for nets [i] based on (9, 42, 192)-net in base 64, using
- t-expansion [i] based on (93, 126, 576)-net in base 4, using
(95, 127, 1227)-Net over F4 — Digital
Digital (95, 127, 1227)-net over F4, using
(95, 127, 136215)-Net in Base 4 — Upper bound on s
There is no (95, 127, 136216)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 28948 432669 195151 098515 411220 927563 279842 686945 168070 861668 755222 504038 559013 > 4127 [i]