Best Known (9, 12, s)-Nets in Base 3
(9, 12, 6464)-Net over F3 — Constructive and digital
Digital (9, 12, 6464)-net over F3, using
- net defined by OOA [i] based on linear OOA(312, 6464, F3, 3, 3) (dual of [(6464, 3), 19380, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(312, 6464, F3, 2, 3) (dual of [(6464, 2), 12916, 4]-NRT-code), using
(9, 12, 21284)-Net over F3 — Upper bound on s (digital)
There is no digital (9, 12, 21285)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(312, 21285, F3, 3) (dual of [21285, 21273, 4]-code or 21285-cap in PG(11,3)), but
- doubling the cap [i] would yield 42570-cap in AG(12,3), but
- 6 times the recursive bound from Bierbrauer and Edel [i] would yield 113-cap in AG(6,3), but
- doubling the cap [i] would yield 42570-cap in AG(12,3), but
(9, 12, 88572)-Net in Base 3 — Upper bound on s
There is no (9, 12, 88573)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(312, 88573, S3, 3), but