Best Known (129, 129+108, s)-Nets in Base 4
(129, 129+108, 130)-Net over F4 — Constructive and digital
Digital (129, 237, 130)-net over F4, using
- t-expansion [i] based on digital (105, 237, 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
(129, 129+108, 224)-Net over F4 — Digital
Digital (129, 237, 224)-net over F4, using
(129, 129+108, 3023)-Net in Base 4 — Upper bound on s
There is no (129, 237, 3024)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 49359 242914 876043 536915 881523 815165 064987 587745 508420 470181 114641 554499 249505 051979 906394 105208 910255 555740 721451 127513 566450 548982 037707 425964 > 4237 [i]