Best Known (43−30, 43, s)-Nets in Base 4
(43−30, 43, 30)-Net over F4 — Constructive and digital
Digital (13, 43, 30)-net over F4, using
- net from sequence [i] based on digital (13, 29)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 30, using
- F4 from the 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) = 13 and N(F) ≥ 30, using
(43−30, 43, 33)-Net over F4 — Digital
Digital (13, 43, 33)-net over F4, using
- net from sequence [i] based on digital (13, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 13 and N(F) ≥ 33, using
(43−30, 43, 102)-Net in Base 4 — Upper bound on s
There is no (13, 43, 103)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 84 017692 177820 091474 626224 > 443 [i]
- extracting embedded orthogonal array [i] would yield OA(443, 103, S4, 30), but
- the linear programming bound shows that M ≥ 126192 248039 190038 466119 259112 020487 681472 723343 663318 526710 983775 014092 800000 / 1468 588736 152011 748631 330502 226638 946367 298107 382103 > 443 [i]