Best Known (126, 126+112, s)-Nets in Base 4
(126, 126+112, 130)-Net over F4 — Constructive and digital
Digital (126, 238, 130)-net over F4, using
- t-expansion [i] based on digital (105, 238, 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
(126, 126+112, 203)-Net over F4 — Digital
Digital (126, 238, 203)-net over F4, using
(126, 126+112, 2573)-Net in Base 4 — Upper bound on s
There is no (126, 238, 2574)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 195200 209194 579513 201203 546692 687577 371982 722886 684059 121068 460544 179567 765503 019564 298674 605315 076645 902595 888926 193186 238472 756069 483832 709664 > 4238 [i]