Best Known (49−39, 49, s)-Nets in Base 7
(49−39, 49, 18)-Net over F7 — Constructive and digital
Digital (10, 49, 18)-net over F7, using
- net from sequence [i] based on digital (10, 17)-sequence over F7, using
(49−39, 49, 38)-Net over F7 — Digital
Digital (10, 49, 38)-net over F7, using
- t-expansion [i] based on digital (9, 49, 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
(49−39, 49, 159)-Net in Base 7 — Upper bound on s
There is no (10, 49, 160)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(749, 160, S7, 39), but
- the linear programming bound shows that M ≥ 203 044415 023138 660553 948393 716208 196178 523952 486772 665939 576916 038830 909525 806585 759499 643744 411871 965648 / 720 550436 520092 516065 302065 163682 679814 516017 234057 265532 052687 > 749 [i]