Best Known (166, 258, s)-Nets in Base 4
(166, 258, 200)-Net over F4 — Constructive and digital
Digital (166, 258, 200)-net over F4, using
- t-expansion [i] based on digital (161, 258, 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
(166, 258, 240)-Net in Base 4 — Constructive
(166, 258, 240)-net in base 4, using
- trace code for nets [i] based on (37, 129, 120)-net in base 16, using
- 1 times m-reduction [i] based on (37, 130, 120)-net in base 16, using
- base change [i] based on digital (11, 104, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- base change [i] based on digital (11, 104, 120)-net over F32, using
- 1 times m-reduction [i] based on (37, 130, 120)-net in base 16, using
(166, 258, 542)-Net over F4 — Digital
Digital (166, 258, 542)-net over F4, using
(166, 258, 14247)-Net in Base 4 — Upper bound on s
There is no (166, 258, 14248)-net in base 4, because
- 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]