Best Known (133, 133+116, s)-Nets in Base 4
(133, 133+116, 130)-Net over F4 — Constructive and digital
Digital (133, 249, 130)-net over F4, using
- t-expansion [i] based on digital (105, 249, 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
(133, 133+116, 218)-Net over F4 — Digital
Digital (133, 249, 218)-net over F4, using
(133, 133+116, 2828)-Net in Base 4 — Upper bound on s
There is no (133, 249, 2829)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 824659 777496 964424 826961 252778 804991 279582 646241 930257 708680 998409 703690 244501 740276 894067 475857 189641 319256 011809 112563 057561 275648 782571 247662 557600 > 4249 [i]