Best Known (212−100, 212, s)-Nets in Base 4
(212−100, 212, 130)-Net over F4 — Constructive and digital
Digital (112, 212, 130)-net over F4, using
- t-expansion [i] based on digital (105, 212, 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
(212−100, 212, 182)-Net over F4 — Digital
Digital (112, 212, 182)-net over F4, using
(212−100, 212, 2277)-Net in Base 4 — Upper bound on s
There is no (112, 212, 2278)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 43 350269 502377 216975 986786 523543 459931 956810 483706 758153 051055 722774 467319 214024 752898 162944 641425 484069 159078 756512 621963 078280 > 4212 [i]