Best Known (25−7, 25, s)-Nets in Base 5
(25−7, 25, 520)-Net over F5 — Constructive and digital
Digital (18, 25, 520)-net over F5, using
- net defined by OOA [i] based on linear OOA(525, 520, F5, 7, 7) (dual of [(520, 7), 3615, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(525, 1561, F5, 7) (dual of [1561, 1536, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(525, 1562, F5, 7) (dual of [1562, 1537, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(525, 1561, F5, 7) (dual of [1561, 1536, 8]-code), using
(25−7, 25, 1472)-Net over F5 — Digital
Digital (18, 25, 1472)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(525, 1472, F5, 7) (dual of [1472, 1447, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(525, 1562, F5, 7) (dual of [1562, 1537, 8]-code), using
(25−7, 25, 177451)-Net in Base 5 — Upper bound on s
There is no (18, 25, 177452)-net in base 5, because
- 1 times m-reduction [i] would yield (18, 24, 177452)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 59605 216224 936625 > 524 [i]