Best Known (25, 25+5, s)-Nets in Base 5
(25, 25+5, 39070)-Net over F5 — Constructive and digital
Digital (25, 30, 39070)-net over F5, using
- net defined by OOA [i] based on linear OOA(530, 39070, F5, 5, 5) (dual of [(39070, 5), 195320, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(530, 78141, F5, 5) (dual of [78141, 78111, 6]-code), using
- construction X applied to C([0,2]) ⊂ C([0,1]) [i] based on
- linear OA(529, 78126, F5, 5) (dual of [78126, 78097, 6]-code), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- linear OA(515, 78126, F5, 3) (dual of [78126, 78111, 4]-code or 78126-cap in PG(14,5)), using the expurgated narrow-sense BCH-code C(I) with length 78126 | 514−1, defining interval I = [0,1], and minimum distance d ≥ |{−1,0,1}|+1 = 4 (BCH-bound) [i]
- linear OA(51, 15, F5, 1) (dual of [15, 14, 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 C([0,2]) ⊂ C([0,1]) [i] based on
- OOA 2-folding and stacking with additional row [i] based on linear OA(530, 78141, F5, 5) (dual of [78141, 78111, 6]-code), using
(25, 25+5, 96666)-Net over F5 — Digital
Digital (25, 30, 96666)-net over F5, using
(25, 25+5, large)-Net in Base 5 — Upper bound on s
There is no (25, 30, large)-net in base 5, because
- 3 times m-reduction [i] would yield (25, 27, large)-net in base 5, but