Best Known (56−40, 56, s)-Nets in Base 5
(56−40, 56, 37)-Net over F5 — Constructive and digital
Digital (16, 56, 37)-net over F5, using
- net from sequence [i] based on digital (16, 36)-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 5 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]
(56−40, 56, 40)-Net over F5 — Digital
Digital (16, 56, 40)-net over F5, using
- net from sequence [i] based on digital (16, 39)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 16 and N(F) ≥ 40, using
(56−40, 56, 170)-Net in Base 5 — Upper bound on s
There is no (16, 56, 171)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(556, 171, S5, 40), but
- the linear programming bound shows that M ≥ 1 601108 245615 962249 140250 840509 665702 056358 493971 132642 934223 614588 518103 118985 891342 163085 937500 / 1109 060396 379933 545627 242365 085519 591548 225462 806947 177771 > 556 [i]