Best Known (173−44, 173, s)-Nets in Base 4
(173−44, 173, 531)-Net over F4 — Constructive and digital
Digital (129, 173, 531)-net over F4, using
- 10 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
(173−44, 173, 576)-Net in Base 4 — Constructive
(129, 173, 576)-net in base 4, using
- t-expansion [i] based on (128, 173, 576)-net in base 4, using
- 1 times m-reduction [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
- 1 times m-reduction [i] based on (128, 174, 576)-net in base 4, using
(173−44, 173, 1509)-Net over F4 — Digital
Digital (129, 173, 1509)-net over F4, using
(173−44, 173, 163706)-Net in Base 4 — Upper bound on s
There is no (129, 173, 163707)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 143 357765 046769 770149 054988 087348 316874 592572 731133 607115 775166 224195 899106 759785 949511 210488 374724 431450 > 4173 [i]