Best Known (7, 7+3, s)-Nets in Base 3
(7, 7+3, 1216)-Net over F3 — Constructive and digital
Digital (7, 10, 1216)-net over F3, using
- net defined by OOA [i] based on linear OOA(310, 1216, F3, 3, 3) (dual of [(1216, 3), 3638, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(310, 1216, F3, 2, 3) (dual of [(1216, 2), 2422, 4]-NRT-code), using
(7, 7+3, 2816)-Net over F3 — Upper bound on s (digital)
There is no digital (7, 10, 2817)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(310, 2817, F3, 3) (dual of [2817, 2807, 4]-code or 2817-cap in PG(9,3)), but
- doubling the cap [i] would yield 5634-cap in AG(10,3), but
- discarding factors / shortening the dual code would yield 5633-cap in AG(10,3), but
- 4 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 5633-cap in AG(10,3), but
- doubling the cap [i] would yield 5634-cap in AG(10,3), but
(7, 7+3, 9840)-Net in Base 3 — Upper bound on s
There is no (7, 10, 9841)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(310, 9841, S3, 3), but