Best Known (47, 62, s)-Nets in Base 25
(47, 62, 55807)-Net over F25 — Constructive and digital
Digital (47, 62, 55807)-net over F25, using
- net defined by OOA [i] based on linear OOA(2562, 55807, F25, 15, 15) (dual of [(55807, 15), 837043, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2562, 390650, F25, 15) (dual of [390650, 390588, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2562, 390652, F25, 15) (dual of [390652, 390590, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,4]) [i] based on
- linear OA(2557, 390626, F25, 15) (dual of [390626, 390569, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(2533, 390626, F25, 9) (dual of [390626, 390593, 10]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- linear OA(255, 26, F25, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using
- extended Reed–Solomon code RSe(21,25) [i]
- the expurgated narrow-sense BCH-code C(I) with length 26 | 252−1, defining interval I = [0,2], and minimum distance d ≥ |{−2,−1,0,1,2}|+1 = 6 (BCH-bound) [i]
- algebraic-geometric code AG(F,10P) with degPÂ =Â 2 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26, using the rational function field F25(x) [i]
- algebraic-geometric code AG(F, Q+6P) with degQ = 2 and degPÂ =Â 3 [i] based on function field F/F25 with g(F) = 0 and N(F) ≥ 26 (see above)
- construction X applied to C([0,7]) ⊂ C([0,4]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2562, 390652, F25, 15) (dual of [390652, 390590, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2562, 390650, F25, 15) (dual of [390650, 390588, 16]-code), using
(47, 62, 390959)-Net over F25 — Digital
Digital (47, 62, 390959)-net over F25, using
(47, 62, large)-Net in Base 25 — Upper bound on s
There is no (47, 62, large)-net in base 25, because
- 13 times m-reduction [i] would yield (47, 49, large)-net in base 25, but