Best Known (129, 175, s)-Nets in Base 4
(129, 175, 531)-Net over F4 — Constructive and digital
Digital (129, 175, 531)-net over F4, using
- 8 times m-reduction [i] based on digital (129, 183, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 61, 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, 61, 177)-net over F64, using
(129, 175, 576)-Net in Base 4 — Constructive
(129, 175, 576)-net in base 4, using
- 41 times duplication [i] based on (128, 174, 576)-net in base 4, using
- trace code for nets [i] based on (12, 58, 192)-net in base 64, using
- 5 times m-reduction [i] based on (12, 63, 192)-net in base 64, using
- base change [i] based on digital (3, 54, 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, 54, 192)-net over F128, using
- 5 times m-reduction [i] based on (12, 63, 192)-net in base 64, using
- trace code for nets [i] based on (12, 58, 192)-net in base 64, using
(129, 175, 1312)-Net over F4 — Digital
Digital (129, 175, 1312)-net over F4, using
(129, 175, 119717)-Net in Base 4 — Upper bound on s
There is no (129, 175, 119718)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2293 607509 106114 407290 457556 122114 017497 326083 442724 577965 784739 688355 652960 538348 556688 409494 121270 208400 > 4175 [i]