Best Known (110−99, 110, s)-Nets in Base 7
(110−99, 110, 19)-Net over F7 — Constructive and digital
Digital (11, 110, 19)-net over F7, using
- net from sequence [i] based on digital (11, 18)-sequence over F7, using
(110−99, 110, 38)-Net over F7 — Digital
Digital (11, 110, 38)-net over F7, using
- t-expansion [i] based on digital (9, 110, 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
(110−99, 110, 85)-Net in Base 7 — Upper bound on s
There is no (11, 110, 86)-net in base 7, because
- 37 times m-reduction [i] would yield (11, 73, 86)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(773, 86, S7, 62), but
- the linear programming bound shows that M ≥ 161806 475312 686849 725066 839632 058773 007336 398342 000423 616787 753916 743157 / 3278 044341 > 773 [i]
- extracting embedded orthogonal array [i] would yield OA(773, 86, S7, 62), but