Best Known (12, 12+3, s)-Nets in Base 3
(12, 12+3, 60928)-Net over F3 — Constructive and digital
Digital (12, 15, 60928)-net over F3, using
- net defined by OOA [i] based on linear OOA(315, 60928, F3, 3, 3) (dual of [(60928, 3), 182769, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(315, 60928, F3, 2, 3) (dual of [(60928, 2), 121841, 4]-NRT-code), using
(12, 12+3, 463343)-Net over F3 — Upper bound on s (digital)
There is no digital (12, 15, 463344)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(315, 463344, F3, 3) (dual of [463344, 463329, 4]-code or 463344-cap in PG(14,3)), but
- doubling the cap [i] would yield 926688-cap in AG(15,3), but
- 9 times the recursive bound from Bierbrauer and Edel [i] would yield 113-cap in AG(6,3), but
- doubling the cap [i] would yield 926688-cap in AG(15,3), but
(12, 12+3, 2391483)-Net in Base 3 — Upper bound on s
There is no (12, 15, 2391484)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(315, 2391484, S3, 3), but