Best Known (133, 133+115, s)-Nets in Base 4
(133, 133+115, 130)-Net over F4 — Constructive and digital
Digital (133, 248, 130)-net over F4, using
- t-expansion [i] based on digital (105, 248, 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+115, 221)-Net over F4 — Digital
Digital (133, 248, 221)-net over F4, using
(133, 133+115, 2944)-Net in Base 4 — Upper bound on s
There is no (133, 248, 2945)-net in base 4, because
- 1 times m-reduction [i] would yield (133, 247, 2945)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 51959 168908 370407 404076 367623 533497 835593 047740 993984 071178 148237 241690 997527 573204 585947 179688 861050 397860 134986 311152 064547 657816 237680 941289 765184 > 4247 [i]