Best Known (1, 1+8, s)-Nets in Base 7
(1, 1+8, 13)-Net over F7 — Constructive and digital
Digital (1, 9, 13)-net over F7, using
- 4 times m-reduction [i] based on digital (1, 13, 13)-net over F7, using
(1, 1+8, 13)-Net over F7 — Upper bound on s (digital)
There is no digital (1, 9, 14)-net over F7, because
- 1 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+8, 25)-Net in Base 7 — Upper bound on s
There is no (1, 9, 26)-net in base 7, because
- 2 times m-reduction [i] would yield (1, 7, 26)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(77, 26, S7, 2, 6), but
- the linear programming bound for OOAs shows that M ≥ 284716 109503 / 329362 > 77 [i]
- extracting embedded OOA [i] would yield OOA(77, 26, S7, 2, 6), but