Best Known (259−93, 259, s)-Nets in Base 4
(259−93, 259, 200)-Net over F4 — Constructive and digital
Digital (166, 259, 200)-net over F4, using
- t-expansion [i] based on digital (161, 259, 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
(259−93, 259, 208)-Net in Base 4 — Constructive
(166, 259, 208)-net in base 4, using
- t-expansion [i] based on (165, 259, 208)-net in base 4, using
- 1 times m-reduction [i] based on (165, 260, 208)-net in base 4, using
- trace code for nets [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
- trace code for nets [i] based on (35, 130, 104)-net in base 16, using
- 1 times m-reduction [i] based on (165, 260, 208)-net in base 4, using
(259−93, 259, 531)-Net over F4 — Digital
Digital (166, 259, 531)-net over F4, using
(259−93, 259, 14247)-Net in Base 4 — Upper bound on s
There is no (166, 259, 14248)-net in base 4, because
- 1 times m-reduction [i] would yield (166, 258, 14248)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 215085 475588 780393 436622 919427 988944 211373 120819 238216 263885 040553 026346 274469 981849 602162 295122 502895 787230 675224 713022 399511 558288 566423 413230 147456 623440 > 4258 [i]