Best Known (126, 126+92, s)-Nets in Base 4
(126, 126+92, 130)-Net over F4 — Constructive and digital
Digital (126, 218, 130)-net over F4, using
- t-expansion [i] based on digital (105, 218, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 from the second 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) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(126, 126+92, 266)-Net over F4 — Digital
Digital (126, 218, 266)-net over F4, using
(126, 126+92, 4241)-Net in Base 4 — Upper bound on s
There is no (126, 218, 4242)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 178668 684659 537391 524230 712133 125865 486091 090160 834055 552319 577001 854489 145295 445331 924343 426661 285642 542234 865586 671169 829264 540768 > 4218 [i]