Best Known (25−3, 25, s)-Nets in Base 5
(25−3, 25, large)-Net over F5 — Constructive and digital
Digital (22, 25, large)-net over F5, using
- 59 times duplication [i] based on digital (13, 16, large)-net over F5, using
- net defined by OOA [i] based on linear OOA(516, large, F5, 3, 3), using
- appending kth column [i] based on linear OOA(516, large, F5, 2, 3), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(516, large, F5, 3) (dual of [large, large−16, 4]-code), using
- product of projective cap with 52-ovoid cap in AG(3, 5) [i] based on linear OA(513, 438101, F5, 3) (dual of [438101, 438088, 4]-code or 438101-cap in PG(12,5)), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(516, large, F5, 3) (dual of [large, large−16, 4]-code), using
- appending kth column [i] based on linear OOA(516, large, F5, 2, 3), using
- net defined by OOA [i] based on linear OOA(516, large, F5, 3, 3), using
(25−3, 25, large)-Net in Base 5 — Upper bound on s
There is no (22, 25, large)-net in base 5, because
- 1 times m-reduction [i] would yield (22, 24, large)-net in base 5, but