Best Known (76−23, 76, s)-Nets in Base 25
(76−23, 76, 1423)-Net over F25 — Constructive and digital
Digital (53, 76, 1423)-net over F25, using
- 251 times duplication [i] based on digital (52, 75, 1423)-net over F25, using
- net defined by OOA [i] based on linear OOA(2575, 1423, F25, 23, 23) (dual of [(1423, 23), 32654, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2575, 15654, F25, 23) (dual of [15654, 15579, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2575, 15655, F25, 23) (dual of [15655, 15580, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,7]) [i] based on
- linear OA(2567, 15626, F25, 23) (dual of [15626, 15559, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(2543, 15626, F25, 15) (dual of [15626, 15583, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(258, 29, F25, 7) (dual of [29, 21, 8]-code), using
- construction X applied to AG(F,9P) ⊂ AG(F,10P) [i] based on
- linear OA(257, 26, F25, 7) (dual of [26, 19, 8]-code or 26-arc in PG(6,25)), using algebraic-geometric code AG(F,9P) 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]
- linear OA(255, 26, F25, 5) (dual of [26, 21, 6]-code or 26-arc in PG(4,25)), using 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 (see above)
- 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 AG(F,9P) ⊂ AG(F,10P) [i] based on
- construction X applied to C([0,11]) ⊂ C([0,7]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2575, 15655, F25, 23) (dual of [15655, 15580, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2575, 15654, F25, 23) (dual of [15654, 15579, 24]-code), using
- net defined by OOA [i] based on linear OOA(2575, 1423, F25, 23, 23) (dual of [(1423, 23), 32654, 24]-NRT-code), using
(76−23, 76, 25473)-Net over F25 — Digital
Digital (53, 76, 25473)-net over F25, using
(76−23, 76, large)-Net in Base 25 — Upper bound on s
There is no (53, 76, large)-net in base 25, because
- 21 times m-reduction [i] would yield (53, 55, large)-net in base 25, but