Best Known (76−58, 76, s)-Nets in Base 5
(76−58, 76, 43)-Net over F5 — Constructive and digital
Digital (18, 76, 43)-net over F5, using
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
(76−58, 76, 122)-Net in Base 5 — Upper bound on s
There is no (18, 76, 123)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(576, 123, S5, 58), but
- the linear programming bound shows that M ≥ 921752 401491 279821 109292 829218 117855 556887 335030 304497 367586 826570 406488 835769 345151 563425 311280 752794 118598 103523 254394 531250 / 6 537188 154799 419763 984572 244509 160994 268577 646991 044355 238439 655214 230447 > 576 [i]