Best Known (12, 12+41, s)-Nets in Base 5
(12, 12+41, 33)-Net over F5 — Constructive and digital
Digital (12, 53, 33)-net over F5, using
- net from sequence [i] based on digital (12, 32)-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 1 place 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]
(12, 12+41, 95)-Net in Base 5 — Upper bound on s
There is no (12, 53, 96)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(553, 96, S5, 41), but
- the linear programming bound shows that M ≥ 84 186533 679041 948678 494756 526007 417171 393468 860758 105001 239942 762172 942249 034854 624437 150538 707186 342435 306869 447231 292724 609375 / 7 205071 110217 819586 689819 848441 076161 798390 729318 755209 443221 110336 829722 721982 817244 620063 > 553 [i]