Best Known (11, 11+54, s)-Nets in Base 7
(11, 11+54, 19)-Net over F7 — Constructive and digital
Digital (11, 65, 19)-net over F7, using
- net from sequence [i] based on digital (11, 18)-sequence over F7, using
(11, 11+54, 38)-Net over F7 — Digital
Digital (11, 65, 38)-net over F7, using
- t-expansion [i] based on digital (9, 65, 38)-net over F7, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 9 and N(F) ≥ 38, using
- net from sequence [i] based on digital (9, 37)-sequence over F7, using
(11, 11+54, 124)-Net in Base 7 — Upper bound on s
There is no (11, 65, 125)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(765, 125, S7, 54), but
- the linear programming bound shows that M ≥ 457279 010335 545467 017712 302712 102045 133653 568175 218748 361850 217430 814016 480420 366730 402612 176780 779568 817581 891525 622756 611584 961142 861177 121749 668384 711429 956885 474361 001593 / 53159 835415 917390 608975 012898 769198 782901 229331 909260 781522 547615 237493 396388 305137 858107 838489 697035 979784 501260 024940 > 765 [i]