Best Known (237−106, 237, s)-Nets in Base 4
(237−106, 237, 130)-Net over F4 — Constructive and digital
Digital (131, 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
(237−106, 237, 237)-Net over F4 — Digital
Digital (131, 237, 237)-net over F4, using
(237−106, 237, 3336)-Net in Base 4 — Upper bound on s
There is no (131, 237, 3337)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 49222 974303 822433 816303 807539 964070 744166 650341 387617 834809 084326 362775 389189 108339 723346 158976 164903 643129 248060 087182 981317 053479 851709 916160 > 4237 [i]