Best Known (14, 14+35, s)-Nets in Base 5
(14, 14+35, 35)-Net over F5 — Constructive and digital
Digital (14, 49, 35)-net over F5, using
- net from sequence [i] based on digital (14, 34)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 11, N(F) = 32, and 3 places with degree 2 [i] based on function field F/F5 with g(F) = 11 and N(F) ≥ 32, using an explicitly constructive algebraic function field [i]
(14, 14+35, 39)-Net over F5 — Digital
Digital (14, 49, 39)-net over F5, using
- net from sequence [i] based on digital (14, 38)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 14 and N(F) ≥ 39, using
(14, 14+35, 156)-Net in Base 5 — Upper bound on s
There is no (14, 49, 157)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(549, 157, S5, 35), but
- the linear programming bound shows that M ≥ 193430 657604 769353 813003 341344 636502 970355 793053 190427 599474 787712 097167 968750 / 10 733668 842676 783287 921900 186509 378669 450747 > 549 [i]