Best Known (7, 68, s)-Nets in Base 7
(7, 68, 15)-Net over F7 — Constructive and digital
Digital (7, 68, 15)-net over F7, using
- net from sequence [i] based on digital (7, 14)-sequence over F7, using
(7, 68, 32)-Net over F7 — Digital
Digital (7, 68, 32)-net over F7, using
- net from sequence [i] based on digital (7, 31)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 7 and N(F) ≥ 32, using
(7, 68, 58)-Net over F7 — Upper bound on s (digital)
There is no digital (7, 68, 59)-net over F7, because
- 12 times m-reduction [i] would yield digital (7, 56, 59)-net over F7, but
- extracting embedded orthogonal array [i] would yield linear OA(756, 59, F7, 49) (dual of [59, 3, 50]-code), but
(7, 68, 59)-Net in Base 7 — Upper bound on s
There is no (7, 68, 60)-net in base 7, because
- 13 times m-reduction [i] would yield (7, 55, 60)-net in base 7, but
- extracting embedded orthogonal array [i] would yield OA(755, 60, S7, 48), but
- the linear programming bound shows that M ≥ 392948 425633 075727 327211 671891 403255 967254 645259 / 11 > 755 [i]
- extracting embedded orthogonal array [i] would yield OA(755, 60, S7, 48), but