Best Known (89−22, 89, s)-Nets in Base 25
(89−22, 89, 35513)-Net over F25 — Constructive and digital
Digital (67, 89, 35513)-net over F25, using
- 251 times duplication [i] based on digital (66, 88, 35513)-net over F25, using
- net defined by OOA [i] based on linear OOA(2588, 35513, F25, 22, 22) (dual of [(35513, 22), 781198, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2588, 390643, F25, 22) (dual of [390643, 390555, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2588, 390644, F25, 22) (dual of [390644, 390556, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(2585, 390625, F25, 22) (dual of [390625, 390540, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2569, 390625, F25, 18) (dual of [390625, 390556, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(253, 19, F25, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,25) or 19-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(2588, 390644, F25, 22) (dual of [390644, 390556, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(2588, 390643, F25, 22) (dual of [390643, 390555, 23]-code), using
- net defined by OOA [i] based on linear OOA(2588, 35513, F25, 22, 22) (dual of [(35513, 22), 781198, 23]-NRT-code), using
(89−22, 89, 390649)-Net over F25 — Digital
Digital (67, 89, 390649)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2589, 390649, F25, 22) (dual of [390649, 390560, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(2585, 390625, F25, 22) (dual of [390625, 390540, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(2565, 390625, F25, 17) (dual of [390625, 390560, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(254, 24, F25, 4) (dual of [24, 20, 5]-code or 24-arc in PG(3,25)), using
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- Reed–Solomon code RS(21,25) [i]
- discarding factors / shortening the dual code based on linear OA(254, 25, F25, 4) (dual of [25, 21, 5]-code or 25-arc in PG(3,25)), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
(89−22, 89, large)-Net in Base 25 — Upper bound on s
There is no (67, 89, large)-net in base 25, because
- 20 times m-reduction [i] would yield (67, 69, large)-net in base 25, but