Best Known (5, 8, s)-Nets in Base 3
(5, 8, 248)-Net over F3 — Constructive and digital
Digital (5, 8, 248)-net over F3, using
- net defined by OOA [i] based on linear OOA(38, 248, F3, 3, 3) (dual of [(248, 3), 736, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(38, 248, F3, 2, 3) (dual of [(248, 2), 488, 4]-NRT-code), using
(5, 8, 386)-Net over F3 — Upper bound on s (digital)
There is no digital (5, 8, 387)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(38, 387, F3, 3) (dual of [387, 379, 4]-code or 387-cap in PG(7,3)), but
- doubling the cap [i] would yield 774-cap in AG(8,3), but
- 2 times the recursive bound from Bierbrauer and Edel [i] would yield 113-cap in AG(6,3), but
- doubling the cap [i] would yield 774-cap in AG(8,3), but
(5, 8, 1092)-Net in Base 3 — Upper bound on s
There is no (5, 8, 1093)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(38, 1093, S3, 3), but