Best Known (16−3, 16, s)-Nets in Base 3
(16−3, 16, 146944)-Net over F3 — Constructive and digital
Digital (13, 16, 146944)-net over F3, using
- net defined by OOA [i] based on linear OOA(316, 146944, F3, 3, 3) (dual of [(146944, 3), 440816, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(316, 146944, F3, 2, 3) (dual of [(146944, 2), 293872, 4]-NRT-code), using
(16−3, 16, 1305705)-Net over F3 — Upper bound on s (digital)
There is no digital (13, 16, 1305706)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(316, 1305706, F3, 3) (dual of [1305706, 1305690, 4]-code or 1305706-cap in PG(15,3)), but
- doubling the cap [i] would yield 2611412-cap in AG(16,3), but
- discarding factors / shortening the dual code would yield 2611411-cap in AG(16,3), but
- 10 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 2611411-cap in AG(16,3), but
- doubling the cap [i] would yield 2611412-cap in AG(16,3), but
(16−3, 16, 7174452)-Net in Base 3 — Upper bound on s
There is no (13, 16, 7174453)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(316, 7174453, S3, 3), but