Best Known (164, 256, s)-Nets in Base 4
(164, 256, 200)-Net over F4 — Constructive and digital
Digital (164, 256, 200)-net over F4, using
- t-expansion [i] based on digital (161, 256, 200)-net over F4, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
(164, 256, 208)-Net in Base 4 — Constructive
(164, 256, 208)-net in base 4, using
- 2 times m-reduction [i] based on (164, 258, 208)-net in base 4, using
- trace code for nets [i] based on (35, 129, 104)-net in base 16, using
- 1 times m-reduction [i] based on (35, 130, 104)-net in base 16, using
- base change [i] based on digital (9, 104, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- base change [i] based on digital (9, 104, 104)-net over F32, using
- 1 times m-reduction [i] based on (35, 130, 104)-net in base 16, using
- trace code for nets [i] based on (35, 129, 104)-net in base 16, using
(164, 256, 524)-Net over F4 — Digital
Digital (164, 256, 524)-net over F4, using
(164, 256, 13411)-Net in Base 4 — Upper bound on s
There is no (164, 256, 13412)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 13425 334292 807071 210187 281565 601618 139956 801577 902212 010056 421498 197070 555771 891015 101087 605985 429326 897926 926057 942453 108692 683949 839430 582241 746328 494384 > 4256 [i]