Best Known (42−15, 42, s)-Nets in Base 25
(42−15, 42, 1115)-Net over F25 — Constructive and digital
Digital (27, 42, 1115)-net over F25, using
- net defined by OOA [i] based on linear OOA(2542, 1115, F25, 15, 15) (dual of [(1115, 15), 16683, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2542, 7806, F25, 15) (dual of [7806, 7764, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2542, 7812, F25, 15) (dual of [7812, 7770, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2542, 7806, F25, 15) (dual of [7806, 7764, 16]-code), using
(42−15, 42, 6049)-Net over F25 — Digital
Digital (27, 42, 6049)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2542, 6049, F25, 15) (dual of [6049, 6007, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2542, 7812, F25, 15) (dual of [7812, 7770, 16]-code), using
(42−15, 42, large)-Net in Base 25 — Upper bound on s
There is no (27, 42, large)-net in base 25, because
- 13 times m-reduction [i] would yield (27, 29, large)-net in base 25, but