Best Known (10, 10+3, s)-Nets in Base 3
(10, 10+3, 13312)-Net over F3 — Constructive and digital
Digital (10, 13, 13312)-net over F3, using
- net defined by OOA [i] based on linear OOA(313, 13312, F3, 3, 3) (dual of [(13312, 3), 39923, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(313, 13312, F3, 2, 3) (dual of [(13312, 2), 26611, 4]-NRT-code), using
(10, 10+3, 59118)-Net over F3 — Upper bound on s (digital)
There is no digital (10, 13, 59119)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(313, 59119, F3, 3) (dual of [59119, 59106, 4]-code or 59119-cap in PG(12,3)), but
- doubling the cap [i] would yield 118238-cap in AG(13,3), but
- 7 times the recursive bound from Bierbrauer and Edel [i] would yield 113-cap in AG(6,3), but
- doubling the cap [i] would yield 118238-cap in AG(13,3), but
(10, 10+3, 265719)-Net in Base 3 — Upper bound on s
There is no (10, 13, 265720)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(313, 265720, S3, 3), but