Best Known (10, 52, s)-Nets in Base 8
(10, 52, 46)-Net over F8 — Constructive and digital
Digital (10, 52, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
(10, 52, 189)-Net in Base 8 — Upper bound on s
There is no (10, 52, 190)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(852, 190, S8, 42), but
- the linear programming bound shows that M ≥ 21196 209665 583906 355434 301806 233437 204001 268139 444712 185390 490223 242817 709960 911149 295660 579423 466291 200000 / 222433 493417 494589 066830 158329 321189 485923 482504 299594 108933 > 852 [i]