Best Known (51−38, 51, s)-Nets in Base 5
(51−38, 51, 34)-Net over F5 — Constructive and digital
Digital (13, 51, 34)-net over F5, using
- net from sequence [i] based on digital (13, 33)-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 2 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]
(51−38, 51, 36)-Net over F5 — Digital
Digital (13, 51, 36)-net over F5, using
- net from sequence [i] based on digital (13, 35)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 13 and N(F) ≥ 36, using
(51−38, 51, 125)-Net in Base 5 — Upper bound on s
There is no (13, 51, 126)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(551, 126, S5, 38), but
- the linear programming bound shows that M ≥ 209 123152 692645 519705 515736 303986 546204 664304 073505 759860 753393 822583 264468 869310 803711 414337 158203 125000 000000 / 463 316752 452645 364344 690583 123386 941507 064171 904835 048805 562407 591683 280043 > 551 [i]