Best Known (6, 6+3, s)-Nets in Base 9
(6, 6+3, 68141)-Net over F9 — Constructive and digital
Digital (6, 9, 68141)-net over F9, using
- net defined by OOA [i] based on linear OOA(99, 68141, F9, 3, 3) (dual of [(68141, 3), 204414, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(99, 68141, F9, 2, 3) (dual of [(68141, 2), 136273, 4]-NRT-code), using
(6, 6+3, 2990279)-Net over F9 — Upper bound on s (digital)
There is no digital (6, 9, 2990280)-net over F9, because
- extracting embedded orthogonal array [i] would yield linear OA(99, 2990280, F9, 3) (dual of [2990280, 2990271, 4]-code or 2990280-cap in PG(8,9)), but
- removing affine subspaces [i] would yield
- linear OA(95, 704, F9, 3) (dual of [704, 699, 4]-code or 704-cap in PG(4,9)), but
- 5376-cap in AG(5,9), but
- 2 times the recursive bound from Bierbrauer and Edel [i] would yield 82-cap in AG(3,9), but
- 42570-cap in AG(6,9), but
- base reduction for affine caps [i] would yield 42570-cap in AG(12,3), but
- 6 times the recursive bound from Bierbrauer and Edel [i] would yield 113-cap in AG(6,3), but
- base reduction for affine caps [i] would yield 42570-cap in AG(12,3), but
- 330223-cap in AG(7,9), but
- base reduction for affine caps [i] would yield 330223-cap in AG(14,3), but
- 8 times the recursive bound from Bierbrauer and Edel [i] would yield 113-cap in AG(6,3) (see above)
- base reduction for affine caps [i] would yield 330223-cap in AG(14,3), but
- 2611411-cap in AG(8,9), but
- base reduction for affine caps [i] 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) (see above)
- base reduction for affine caps [i] would yield 2611411-cap in AG(16,3), but
- removing affine subspaces [i] would yield
(6, 6+3, 5380839)-Net in Base 9 — Upper bound on s
There is no (6, 9, 5380840)-net in base 9, because
- extracting embedded orthogonal array [i] would yield OA(99, 5380840, S9, 3), but