Best Known (12, 12+36, s)-Nets in Base 5
(12, 12+36, 33)-Net over F5 — Constructive and digital
Digital (12, 48, 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+36, 116)-Net in Base 5 — Upper bound on s
There is no (12, 48, 117)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(548, 117, S5, 36), but
- the linear programming bound shows that M ≥ 857737 153103 885496 330490 271513 380662 269378 253967 687124 391832 458681 463089 622229 745145 887136 459350 585937 500000 / 238 558124 760736 411982 747178 579992 386558 436129 608373 218223 385627 584585 285287 > 548 [i]