Best Known (121, 121+42, s)-Nets in Base 4
(121, 121+42, 531)-Net over F4 — Constructive and digital
Digital (121, 163, 531)-net over F4, using
- 8 times m-reduction [i] based on digital (121, 171, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 57, 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, 57, 177)-net over F64, using
(121, 121+42, 576)-Net in Base 4 — Constructive
(121, 163, 576)-net in base 4, using
- 2 times m-reduction [i] based on (121, 165, 576)-net in base 4, using
- trace code for nets [i] based on (11, 55, 192)-net in base 64, using
- 1 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
- base change [i] based on digital (3, 48, 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, 48, 192)-net over F128, using
- 1 times m-reduction [i] based on (11, 56, 192)-net in base 64, using
- trace code for nets [i] based on (11, 55, 192)-net in base 64, using
(121, 121+42, 1352)-Net over F4 — Digital
Digital (121, 163, 1352)-net over F4, using
(121, 121+42, 136285)-Net in Base 4 — Upper bound on s
There is no (121, 163, 136286)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 136 714976 055567 971405 219349 031050 110853 792873 836240 388241 654225 333466 361872 335879 626873 100132 605979 > 4163 [i]