Best Known (166, 260, s)-Nets in Base 4
(166, 260, 200)-Net over F4 — Constructive and digital
Digital (166, 260, 200)-net over F4, using
- t-expansion [i] based on digital (161, 260, 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, 260, 208)-Net in Base 4 — Constructive
(166, 260, 208)-net in base 4, using
- t-expansion [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
(166, 260, 520)-Net over F4 — Digital
Digital (166, 260, 520)-net over F4, using
(166, 260, 13068)-Net in Base 4 — Upper bound on s
There is no (166, 260, 13069)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3 432865 460689 257245 545032 479030 989826 274751 583292 065695 395779 040325 004165 769850 217515 617969 892022 430198 723073 995108 873748 061610 243686 835496 591675 319125 715200 > 4260 [i]