Best Known (14, 54, s)-Nets in Base 5
(14, 54, 35)-Net over F5 — Constructive and digital
Digital (14, 54, 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, 54, 39)-Net over F5 — Digital
Digital (14, 54, 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, 54, 134)-Net in Base 5 — Upper bound on s
There is no (14, 54, 135)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(554, 135, S5, 40), but
- the linear programming bound shows that M ≥ 53663 270868 891151 346920 373310 656831 792532 665841 131162 284148 653993 761469 392413 181457 982369 693127 111531 794071 197509 765625 / 950 013894 278175 311311 543163 382767 955608 208007 141598 072744 126896 257952 396992 626809 > 554 [i]