Best Known (51−37, 51, s)-Nets in Base 5
(51−37, 51, 35)-Net over F5 — Constructive and digital
Digital (14, 51, 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]
(51−37, 51, 39)-Net over F5 — Digital
Digital (14, 51, 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
(51−37, 51, 147)-Net in Base 5 — Upper bound on s
There is no (14, 51, 148)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(551, 148, S5, 37), but
- the linear programming bound shows that M ≥ 15 663939 012784 640472 671043 836508 016647 200581 486278 265608 961849 238767 172209 918498 992919 921875 / 33 930477 809461 421279 356068 839821 557007 128106 266211 889987 > 551 [i]