Best Known (82−64, 82, s)-Nets in Base 5
(82−64, 82, 43)-Net over F5 — Constructive and digital
Digital (18, 82, 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]
(82−64, 82, 101)-Net in Base 5 — Upper bound on s
There is no (18, 82, 102)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(582, 102, S5, 64), but
- the linear programming bound shows that M ≥ 2 883275 757249 475288 831953 013438 287591 885256 233581 458218 395709 991455 078125 / 1000 229378 337189 > 582 [i]