Best Known (167−42, 167, s)-Nets in Base 4
(167−42, 167, 531)-Net over F4 — Constructive and digital
Digital (125, 167, 531)-net over F4, using
- 10 times m-reduction [i] based on digital (125, 177, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 59, 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, 59, 177)-net over F64, using
(167−42, 167, 648)-Net in Base 4 — Constructive
(125, 167, 648)-net in base 4, using
- 1 times m-reduction [i] based on (125, 168, 648)-net in base 4, using
- trace code for nets [i] based on (13, 56, 216)-net in base 64, using
- base change [i] based on digital (5, 48, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 48, 216)-net over F128, using
- trace code for nets [i] based on (13, 56, 216)-net in base 64, using
(167−42, 167, 1545)-Net over F4 — Digital
Digital (125, 167, 1545)-net over F4, using
(167−42, 167, 177476)-Net in Base 4 — Upper bound on s
There is no (125, 167, 177477)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 34999 320863 767619 185047 484319 512411 317265 876018 522632 342570 093730 509726 593898 275745 779316 763462 437232 > 4167 [i]