Best Known (81−29, 81, s)-Nets in Base 25
(81−29, 81, 557)-Net over F25 — Constructive and digital
Digital (52, 81, 557)-net over F25, using
- net defined by OOA [i] based on linear OOA(2581, 557, F25, 29, 29) (dual of [(557, 29), 16072, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2581, 7799, F25, 29) (dual of [7799, 7718, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2581, 7812, F25, 29) (dual of [7812, 7731, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(2581, 7799, F25, 29) (dual of [7799, 7718, 30]-code), using
(81−29, 81, 6300)-Net over F25 — Digital
Digital (52, 81, 6300)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2581, 6300, F25, 29) (dual of [6300, 6219, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(2581, 7812, F25, 29) (dual of [7812, 7731, 30]-code), using
(81−29, 81, large)-Net in Base 25 — Upper bound on s
There is no (52, 81, large)-net in base 25, because
- 27 times m-reduction [i] would yield (52, 54, large)-net in base 25, but