Best Known (6, 9, s)-Nets in Base 7
(6, 9, 21555)-Net over F7 — Constructive and digital
Digital (6, 9, 21555)-net over F7, using
- net defined by OOA [i] based on linear OOA(79, 21555, F7, 3, 3) (dual of [(21555, 3), 64656, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(79, 21555, F7, 2, 3) (dual of [(21555, 2), 43101, 4]-NRT-code), using
(6, 9, 483575)-Net over F7 — Upper bound on s (digital)
There is no digital (6, 9, 483576)-net over F7, because
- extracting embedded orthogonal array [i] would yield linear OA(79, 483576, F7, 3) (dual of [483576, 483567, 4]-code or 483576-cap in PG(8,7)), but
- removing affine subspaces [i] would yield
- linear OA(76, 1659, F7, 3) (dual of [1659, 1653, 4]-code or 1659-cap in PG(5,7)), but
- 9735-cap in AG(6,7), but
- 2 times the recursive bound from Bierbrauer and Edel [i] would yield 239-cap in AG(4,7), but
- 62933-cap in AG(7,7), but
- 3 times the recursive bound from Bierbrauer and Edel [i] would yield 239-cap in AG(4,7) (see above)
- 409252-cap in AG(8,7), but
- 4 times the recursive bound from Bierbrauer and Edel [i] would yield 239-cap in AG(4,7) (see above)
- removing affine subspaces [i] would yield
(6, 9, 960799)-Net in Base 7 — Upper bound on s
There is no (6, 9, 960800)-net in base 7, because
- extracting embedded orthogonal array [i] would yield OA(79, 960800, S7, 3), but