Best Known (14, 14+49, s)-Nets in Base 5
(14, 14+49, 35)-Net over F5 — Constructive and digital
Digital (14, 63, 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+49, 39)-Net over F5 — Digital
Digital (14, 63, 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+49, 90)-Net in Base 5 — Upper bound on s
There is no (14, 63, 91)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(563, 91, S5, 49), but
- the linear programming bound shows that M ≥ 155312 762779 283221 691961 451582 653097 602815 250866 115093 231201 171875 / 1343 586115 448394 275304 > 563 [i]