Best Known (3, 3+7, s)-Nets in Base 3
(3, 3+7, 11)-Net over F3 — Constructive and digital
Digital (3, 10, 11)-net over F3, using
(3, 3+7, 15)-Net over F3 — Upper bound on s (digital)
There is no digital (3, 10, 16)-net over F3, because
- 1 times m-reduction [i] would yield digital (3, 9, 16)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(39, 16, F3, 6) (dual of [16, 7, 7]-code), but
- “vE2†bound on codes from Brouwer’s database [i]
- extracting embedded orthogonal array [i] would yield linear OA(39, 16, F3, 6) (dual of [16, 7, 7]-code), but
(3, 3+7, 21)-Net in Base 3 — Upper bound on s
There is no (3, 10, 22)-net in base 3, because
- 1 times m-reduction [i] would yield (3, 9, 22)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(39, 22, S3, 2, 6), but
- the linear programming bound for OOAs shows that M ≥ 287963 682390 / 14 415719 > 39 [i]
- extracting embedded OOA [i] would yield OOA(39, 22, S3, 2, 6), but