Best Known (1, 1+12, s)-Nets in Base 7
(1, 1+12, 13)-Net over F7 — Constructive and digital
(1, 1+12, 13)-Net over F7 — Upper bound on s (digital)
There is no digital (1, 13, 14)-net over F7, because
- 5 times m-reduction [i] would yield digital (1, 8, 14)-net over F7, but
- extracting embedded orthogonal array [i] would yield linear OA(78, 14, F7, 7) (dual of [14, 6, 8]-code), but
- “MPa†bound on codes from Brouwer’s database [i]
- extracting embedded orthogonal array [i] would yield linear OA(78, 14, F7, 7) (dual of [14, 6, 8]-code), but
(1, 1+12, 18)-Net in Base 7 — Upper bound on s
There is no (1, 13, 19)-net in base 7, because
- extracting embedded OOA [i] would yield OOA(713, 19, S7, 2, 12), but
- the linear programming bound for OOAs shows that M ≥ 3645 449016 563375 / 36107 > 713 [i]