Best Known (50−37, 50, s)-Nets in Base 4
(50−37, 50, 30)-Net over F4 — Constructive and digital
Digital (13, 50, 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
(50−37, 50, 33)-Net over F4 — Digital
Digital (13, 50, 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
(50−37, 50, 67)-Net in Base 4 — Upper bound on s
There is no (13, 50, 68)-net in base 4, because
- extracting embedded orthogonal array [i] would yield OA(450, 68, S4, 37), but
- the linear programming bound shows that M ≥ 11357 650917 546516 093958 121792 521354 870784 / 7451 279381 > 450 [i]