Best Known (6, 9, s)-Nets in Base 8
(6, 9, 45174)-Net over F8 — Constructive and digital
Digital (6, 9, 45174)-net over F8, using
- net defined by OOA [i] based on linear OOA(89, 45174, F8, 3, 3) (dual of [(45174, 3), 135513, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(89, 45174, F8, 2, 3) (dual of [(45174, 2), 90339, 4]-NRT-code), using
(6, 9, 1495166)-Net over F8 — Upper bound on s (digital)
There is no digital (6, 9, 1495167)-net over F8, because
- extracting embedded orthogonal array [i] would yield linear OA(89, 1495167, F8, 3) (dual of [1495167, 1495158, 4]-code or 1495167-cap in PG(8,8)), but
- removing affine subspaces [i] would yield
- linear OA(85, 494, F8, 3) (dual of [494, 489, 4]-code or 494-cap in PG(4,8)), but
- 3284-cap in AG(5,8), but
- 2 times the recursive bound from Bierbrauer and Edel [i] would yield 65-cap in AG(3,8), but
- 23874-cap in AG(6,8), but
- 3 times the recursive bound from Bierbrauer and Edel [i] would yield 65-cap in AG(3,8) (see above)
- 175045-cap in AG(7,8), but
- 4 times the recursive bound from Bierbrauer and Edel [i] would yield 65-cap in AG(3,8) (see above)
- 1292474-cap in AG(8,8), but
- 5 times the recursive bound from Bierbrauer and Edel [i] would yield 65-cap in AG(3,8) (see above)
- removing affine subspaces [i] would yield
(6, 9, 2396744)-Net in Base 8 — Upper bound on s
There is no (6, 9, 2396745)-net in base 8, because
- extracting embedded orthogonal array [i] would yield OA(89, 2396745, S8, 3), but