Best Known (14−3, 14, s)-Nets in Base 3
(14−3, 14, 30464)-Net over F3 — Constructive and digital
Digital (11, 14, 30464)-net over F3, using
- net defined by OOA [i] based on linear OOA(314, 30464, F3, 3, 3) (dual of [(30464, 3), 91378, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(314, 30464, F3, 2, 3) (dual of [(30464, 2), 60914, 4]-NRT-code), using
(14−3, 14, 165111)-Net over F3 — Upper bound on s (digital)
There is no digital (11, 14, 165112)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(314, 165112, F3, 3) (dual of [165112, 165098, 4]-code or 165112-cap in PG(13,3)), but
- doubling the cap [i] would yield 330224-cap in AG(14,3), but
- discarding factors / shortening the dual code would yield 330223-cap in AG(14,3), but
- 8 times the recursive bound from Bierbrauer and Edel [i] would yield 113-cap in AG(6,3), but
- discarding factors / shortening the dual code would yield 330223-cap in AG(14,3), but
- doubling the cap [i] would yield 330224-cap in AG(14,3), but
(14−3, 14, 797160)-Net in Base 3 — Upper bound on s
There is no (11, 14, 797161)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(314, 797161, S3, 3), but