Best Known (125, 125+44, s)-Nets in Base 4
(125, 125+44, 531)-Net over F4 — Constructive and digital
Digital (125, 169, 531)-net over F4, using
- 8 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
(125, 125+44, 576)-Net in Base 4 — Constructive
(125, 169, 576)-net in base 4, using
- 41 times duplication [i] based on (124, 168, 576)-net in base 4, using
- t-expansion [i] based on (123, 168, 576)-net in base 4, using
- trace code for nets [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
- trace code for nets [i] based on (11, 56, 192)-net in base 64, using
- t-expansion [i] based on (123, 168, 576)-net in base 4, using
(125, 125+44, 1329)-Net over F4 — Digital
Digital (125, 169, 1329)-net over F4, using
(125, 125+44, 127229)-Net in Base 4 — Upper bound on s
There is no (125, 169, 127230)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 560027 891545 174492 445006 019264 857414 000411 221021 554348 330944 512538 373123 342975 434274 021297 714370 857436 > 4169 [i]