Best Known (25, 29, s)-Nets in Base 5
(25, 29, 976572)-Net over F5 — Constructive and digital
Digital (25, 29, 976572)-net over F5, using
- net defined by OOA [i] based on linear OOA(529, 976572, F5, 4, 4) (dual of [(976572, 4), 3906259, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(529, 976572, F5, 3, 4) (dual of [(976572, 3), 2929687, 5]-NRT-code), using
- OA 2-folding and stacking [i] based on linear OA(529, 1953144, F5, 4) (dual of [1953144, 1953115, 5]-code), using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- linear OA(528, 1953125, F5, 4) (dual of [1953125, 1953097, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(510, 1953125, F5, 2) (dual of [1953125, 1953115, 3]-code), using an extension Ce(1) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,1], and designed minimum distance d ≥ |I|+1 = 2 [i]
- linear OA(51, 19, F5, 1) (dual of [19, 18, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(3) ⊂ Ce(1) [i] based on
- OA 2-folding and stacking [i] based on linear OA(529, 1953144, F5, 4) (dual of [1953144, 1953115, 5]-code), using
- appending kth column [i] based on linear OOA(529, 976572, F5, 3, 4) (dual of [(976572, 3), 2929687, 5]-NRT-code), using
(25, 29, 2594383)-Net over F5 — Digital
Digital (25, 29, 2594383)-net over F5, using
- net defined by OOA [i] based on linear OOA(529, 2594383, F5, 4, 4) (dual of [(2594383, 4), 10377503, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(529, 2594383, F5, 3, 4) (dual of [(2594383, 3), 7783120, 5]-NRT-code), using
(25, 29, large)-Net in Base 5 — Upper bound on s
There is no (25, 29, large)-net in base 5, because
- 2 times m-reduction [i] would yield (25, 27, large)-net in base 5, but