Best Known (9, 9+44, s)-Nets in Base 7
(9, 9+44, 17)-Net over F7 — Constructive and digital
Digital (9, 53, 17)-net over F7, using
- net from sequence [i] based on digital (9, 16)-sequence over F7, using
(9, 9+44, 38)-Net over F7 — Digital
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
(9, 9+44, 115)-Net in Base 7 — Upper bound on s
There is no (9, 53, 116)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(753, 116, S7, 44), but
- the linear programming bound shows that M ≥ 1 821265 863047 547758 388873 609653 333965 000266 572790 061222 143079 321905 157878 203433 357059 292149 639067 213351 173091 820480 749615 / 2881 632204 485330 644711 003017 826948 329991 045505 427169 476080 375988 334746 548407 > 753 [i]