Best Known (57−47, 57, s)-Nets in Base 8
(57−47, 57, 46)-Net over F8 — Constructive and digital
Digital (10, 57, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
(57−47, 57, 175)-Net in Base 8 — Upper bound on s
There is no (10, 57, 176)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(857, 176, S8, 47), but
- the linear programming bound shows that M ≥ 110795 077329 228599 218452 609759 120122 047067 697886 834518 855448 201951 079806 280165 038461 024210 558886 600241 721429 196800 / 33 575208 523191 054990 676598 053406 603811 238738 500943 580257 285163 > 857 [i]