Best Known (7−5, 7, s)-Nets in Base 3
(7−5, 7, 11)-Net over F3 — Constructive and digital
Digital (2, 7, 11)-net over F3, using
(7−5, 7, 14)-Net over F3 — Upper bound on s (digital)
There is no digital (2, 7, 15)-net over F3, because
- 1 times m-reduction [i] would yield digital (2, 6, 15)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(36, 15, F3, 4) (dual of [15, 9, 5]-code), but
- “vE2†bound on codes from Brouwer’s database [i]
- extracting embedded orthogonal array [i] would yield linear OA(36, 15, F3, 4) (dual of [15, 9, 5]-code), but
(7−5, 7, 16)-Net in Base 3 — Upper bound on s
There is no (2, 7, 17)-net in base 3, because
- extracting embedded OOA [i] would yield OOA(37, 17, S3, 2, 5), but
- the linear programming bound for OOAs shows that M ≥ 129 947895 / 55163 > 37 [i]