Best Known (6, 6+3, s)-Nets in Base 3
(6, 6+3, 532)-Net over F3 — Constructive and digital
Digital (6, 9, 532)-net over F3, using
- net defined by OOA [i] based on linear OOA(39, 532, F3, 3, 3) (dual of [(532, 3), 1587, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(39, 532, F3, 2, 3) (dual of [(532, 2), 1055, 4]-NRT-code), using
(6, 6+3, 1037)-Net over F3 — Upper bound on s (digital)
There is no digital (6, 9, 1038)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(39, 1038, F3, 3) (dual of [1038, 1029, 4]-code or 1038-cap in PG(8,3)), but
- doubling the cap [i] would yield 2076-cap in AG(9,3), but
- 3 times the recursive bound from Bierbrauer and Edel [i] would yield 113-cap in AG(6,3), but
- doubling the cap [i] would yield 2076-cap in AG(9,3), but
(6, 6+3, 3279)-Net in Base 3 — Upper bound on s
There is no (6, 9, 3280)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(39, 3280, S3, 3), but