Best Known (14, 14+55, s)-Nets in Base 5
(14, 14+55, 35)-Net over F5 — Constructive and digital
Digital (14, 69, 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+55, 39)-Net over F5 — Digital
Digital (14, 69, 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+55, 79)-Net in Base 5 — Upper bound on s
There is no (14, 69, 80)-net in base 5, because
- 1 times m-reduction [i] would yield (14, 68, 80)-net in base 5, but
- extracting embedded orthogonal array [i] would yield OA(568, 80, S5, 54), but
- the linear programming bound shows that M ≥ 1360 149624 833194 466344 554740 544481 319375 336170 196533 203125 / 3265 361781 > 568 [i]
- extracting embedded orthogonal array [i] would yield OA(568, 80, S5, 54), but