Best Known (26, 26+5, s)-Nets in Base 5
(26, 26+5, 39092)-Net over F5 — Constructive and digital
Digital (26, 31, 39092)-net over F5, using
- net defined by OOA [i] based on linear OOA(531, 39092, F5, 6, 5) (dual of [(39092, 6), 234521, 6]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(531, 39093, F5, 2, 5) (dual of [(39093, 2), 78155, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(53, 31, F5, 2, 2) (dual of [(31, 2), 59, 3]-NRT-code), using
- appending kth column [i] based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- Hamming code H(3,5) [i]
- appending kth column [i] based on linear OA(53, 31, F5, 2) (dual of [31, 28, 3]-code), using
- linear OOA(528, 39062, F5, 2, 5) (dual of [(39062, 2), 78096, 6]-NRT-code), using
- OOA 2-folding [i] based on linear OA(528, 78124, F5, 5) (dual of [78124, 78096, 6]-code), using
- 1 times truncation [i] based on linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using
- an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- 1 times truncation [i] based on linear OA(529, 78125, F5, 6) (dual of [78125, 78096, 7]-code), using
- OOA 2-folding [i] based on linear OA(528, 78124, F5, 5) (dual of [78124, 78096, 6]-code), using
- linear OOA(53, 31, F5, 2, 2) (dual of [(31, 2), 59, 3]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(531, 39093, F5, 2, 5) (dual of [(39093, 2), 78155, 6]-NRT-code), using
(26, 26+5, 144549)-Net over F5 — Digital
Digital (26, 31, 144549)-net over F5, using
(26, 26+5, large)-Net in Base 5 — Upper bound on s
There is no (26, 31, large)-net in base 5, because
- 3 times m-reduction [i] would yield (26, 28, large)-net in base 5, but