Best Known (133, 179, s)-Nets in Base 4
(133, 179, 531)-Net over F4 — Constructive and digital
Digital (133, 179, 531)-net over F4, using
- 10 times m-reduction [i] based on digital (133, 189, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 63, 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, 63, 177)-net over F64, using
(133, 179, 576)-Net in Base 4 — Constructive
(133, 179, 576)-net in base 4, using
- t-expansion [i] based on (132, 179, 576)-net in base 4, using
- 1 times m-reduction [i] based on (132, 180, 576)-net in base 4, using
- trace code for nets [i] based on (12, 60, 192)-net in base 64, using
- 3 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
- 3 times m-reduction [i] based on (12, 63, 192)-net in base 64, using
- trace code for nets [i] based on (12, 60, 192)-net in base 64, using
- 1 times m-reduction [i] based on (132, 180, 576)-net in base 4, using
(133, 179, 1481)-Net over F4 — Digital
Digital (133, 179, 1481)-net over F4, using
(133, 179, 152362)-Net in Base 4 — Upper bound on s
There is no (133, 179, 152363)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 587147 095712 386803 696445 635104 219691 429203 935140 158807 423669 775460 307892 101757 641989 528674 048146 386144 236160 > 4179 [i]