Best Known (92−22, 92, s)-Nets in Base 25
(92−22, 92, 35514)-Net over F25 — Constructive and digital
Digital (70, 92, 35514)-net over F25, using
- 251 times duplication [i] based on digital (69, 91, 35514)-net over F25, using
- net defined by OOA [i] based on linear OOA(2591, 35514, F25, 22, 22) (dual of [(35514, 22), 781217, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(2591, 390654, F25, 22) (dual of [390654, 390563, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [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(2561, 390625, F25, 16) (dual of [390625, 390564, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(256, 29, F25, 5) (dual of [29, 23, 6]-code), using
- construction for [s, s−6, 6]-code from [s, 3, s−3]-code [i] based on linear OA(2526, 29, F25, 25) (dual of [29, 3, 26]-code), using
- construction X applied to C1 ⊂ C0 [i] based on
- linear OA(2525, 26, F25, 25) (dual of [26, 1, 26]-code or 26-arc in PG(24,25)), using code C1 for u = 2 by de Boer and Brouwer [i]
- linear OA(2523, 26, F25, 23) (dual of [26, 3, 24]-code or 26-arc in PG(22,25)), using code C0 for u = 2 by de Boer and Brouwer [i]
- linear OA(251, 3, F25, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C1 ⊂ C0 [i] based on
- construction for [s, s−6, 6]-code from [s, 3, s−3]-code [i] based on linear OA(2526, 29, F25, 25) (dual of [29, 3, 26]-code), using
- construction X applied to Ce(21) ⊂ Ce(15) [i] based on
- OA 11-folding and stacking [i] based on linear OA(2591, 390654, F25, 22) (dual of [390654, 390563, 23]-code), using
- net defined by OOA [i] based on linear OOA(2591, 35514, F25, 22, 22) (dual of [(35514, 22), 781217, 23]-NRT-code), using
(92−22, 92, 481503)-Net over F25 — Digital
Digital (70, 92, 481503)-net over F25, using
(92−22, 92, large)-Net in Base 25 — Upper bound on s
There is no (70, 92, large)-net in base 25, because
- 20 times m-reduction [i] would yield (70, 72, large)-net in base 25, but