Best Known (65−52, 65, s)-Nets in Base 9
(65−52, 65, 64)-Net over F9 — Constructive and digital
Digital (13, 65, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
(65−52, 65, 288)-Net in Base 9 — Upper bound on s
There is no (13, 65, 289)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(965, 289, S9, 52), but
- the linear programming bound shows that M ≥ 40485 504541 504777 871609 954566 831876 659509 254283 068602 558517 621054 931333 031201 869538 286529 051209 384428 388969 040481 229444 574533 779318 750000 / 368 223009 858384 319213 473055 655893 095512 815101 908418 906065 904265 896532 439183 > 965 [i]