Best Known (7, 7+3, s)-Nets in Base 5
(7, 7+3, 17124)-Net over F5 — Constructive and digital
Digital (7, 10, 17124)-net over F5, using
- net defined by OOA [i] based on linear OOA(510, 17124, F5, 3, 3) (dual of [(17124, 3), 51362, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(510, 17124, F5, 2, 3) (dual of [(17124, 2), 34238, 4]-NRT-code), using
(7, 7+3, 206584)-Net over F5 — Upper bound on s (digital)
There is no digital (7, 10, 206585)-net over F5, because
- extracting embedded orthogonal array [i] would yield linear OA(510, 206585, F5, 3) (dual of [206585, 206575, 4]-code or 206585-cap in PG(9,5)), but
- removing affine subspaces [i] would yield
- linear OA(56, 435, F5, 3) (dual of [435, 429, 4]-code or 435-cap in PG(5,5)), but
- 1719-cap in AG(6,5), but
- 2 times the recursive bound from Bierbrauer and Edel [i] would yield 89-cap in AG(4,5), but
- 7740-cap in AG(7,5), but
- 3 times the recursive bound from Bierbrauer and Edel [i] would yield 89-cap in AG(4,5) (see above)
- 35209-cap in AG(8,5), but
- 4 times the recursive bound from Bierbrauer and Edel [i] would yield 89-cap in AG(4,5) (see above)
- 161486-cap in AG(9,5), but
- 5 times the recursive bound from Bierbrauer and Edel [i] would yield 89-cap in AG(4,5) (see above)
- removing affine subspaces [i] would yield
(7, 7+3, 488280)-Net in Base 5 — Upper bound on s
There is no (7, 10, 488281)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(510, 488281, S5, 3), but