Best Known (10, 10+43, s)-Nets in Base 7
(10, 10+43, 18)-Net over F7 — Constructive and digital
Digital (10, 53, 18)-net over F7, using
- net from sequence [i] based on digital (10, 17)-sequence over F7, using
(10, 10+43, 38)-Net over F7 — Digital
Digital (10, 53, 38)-net over F7, using
- t-expansion [i] based on digital (9, 53, 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
(10, 10+43, 144)-Net in Base 7 — Upper bound on s
There is no (10, 53, 145)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(753, 145, S7, 43), but
- the linear programming bound shows that M ≥ 56573 395336 845143 449293 238847 399850 474042 111934 612664 687507 110122 836248 224035 666008 035330 620459 055271 762105 368720 / 87 739859 677389 587540 375648 441472 115810 010092 007864 088598 888347 746933 > 753 [i]