Best Known (89−23, 89, s)-Nets in Base 25
(89−23, 89, 35511)-Net over F25 — Constructive and digital
Digital (66, 89, 35511)-net over F25, using
- net defined by OOA [i] based on linear OOA(2589, 35511, F25, 23, 23) (dual of [(35511, 23), 816664, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2589, 390622, F25, 23) (dual of [390622, 390533, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2589, 390625, F25, 23) (dual of [390625, 390536, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(2589, 390625, F25, 23) (dual of [390625, 390536, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2589, 390622, F25, 23) (dual of [390622, 390533, 24]-code), using
(89−23, 89, 260794)-Net over F25 — Digital
Digital (66, 89, 260794)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2589, 260794, F25, 23) (dual of [260794, 260705, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2589, 390625, F25, 23) (dual of [390625, 390536, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(2589, 390625, F25, 23) (dual of [390625, 390536, 24]-code), using
(89−23, 89, large)-Net in Base 25 — Upper bound on s
There is no (66, 89, large)-net in base 25, because
- 21 times m-reduction [i] would yield (66, 68, large)-net in base 25, but