Best Known (14, 14+53, s)-Nets in Base 5
(14, 14+53, 35)-Net over F5 — Constructive and digital
Digital (14, 67, 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+53, 39)-Net over F5 — Digital
Digital (14, 67, 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+53, 80)-Net in Base 5 — Upper bound on s
There is no (14, 67, 81)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(567, 81, S5, 53), but
- the linear programming bound shows that M ≥ 3786 237274 226722 515635 401578 037999 570369 720458 984375 / 50209 > 567 [i]