Best Known (109−96, 109, s)-Nets in Base 7
(109−96, 109, 21)-Net over F7 — Constructive and digital
Digital (13, 109, 21)-net over F7, using
- net from sequence [i] based on digital (13, 20)-sequence over F7, using
(109−96, 109, 48)-Net over F7 — Digital
Digital (13, 109, 48)-net over F7, using
- net from sequence [i] based on digital (13, 47)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 13 and N(F) ≥ 48, using
(109−96, 109, 97)-Net in Base 7 — Upper bound on s
There is no (13, 109, 98)-net in base 7, because
- 22 times m-reduction [i] would yield (13, 87, 98)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(787, 98, S7, 74), but
- the linear programming bound shows that M ≥ 42407 610952 566807 294788 235072 104256 021156 669481 359079 294981 146935 094240 996998 497183 / 1146 522975 > 787 [i]
- extracting embedded orthogonal array [i] would yield OA(787, 98, S7, 74), but