Best Known (8, 11, s)-Nets in Base 5
(8, 11, 43876)-Net over F5 — Constructive and digital
Digital (8, 11, 43876)-net over F5, using
- net defined by OOA [i] based on linear OOA(511, 43876, F5, 3, 3) (dual of [(43876, 3), 131617, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(511, 43876, F5, 2, 3) (dual of [(43876, 2), 87741, 4]-NRT-code), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(511, 43876, F5, 3) (dual of [43876, 43865, 4]-code or 43876-cap in PG(10,5)), using
- appending kth column [i] based on linear OOA(511, 43876, F5, 2, 3) (dual of [(43876, 2), 87741, 4]-NRT-code), using
(8, 11, 952349)-Net over F5 — Upper bound on s (digital)
There is no digital (8, 11, 952350)-net over F5, because
- extracting embedded orthogonal array [i] would yield linear OA(511, 952350, F5, 3) (dual of [952350, 952339, 4]-code or 952350-cap in PG(10,5)), 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)
- 745766-cap in AG(10,5), but
- 6 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
(8, 11, 2441405)-Net in Base 5 — Upper bound on s
There is no (8, 11, 2441406)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(511, 2441406, S5, 3), but