Best Known (71, 94, s)-Nets in Base 25
(71, 94, 35513)-Net over F25 — Constructive and digital
Digital (71, 94, 35513)-net over F25, using
- 252 times duplication [i] based on digital (69, 92, 35513)-net over F25, using
- net defined by OOA [i] based on linear OOA(2592, 35513, F25, 23, 23) (dual of [(35513, 23), 816707, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2592, 390644, F25, 23) (dual of [390644, 390552, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(2592, 390645, F25, 23) (dual of [390645, 390553, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- linear OA(2589, 390626, F25, 23) (dual of [390626, 390537, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(2573, 390626, F25, 19) (dual of [390626, 390553, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(253, 19, F25, 3) (dual of [19, 16, 4]-code or 19-arc in PG(2,25) or 19-cap in PG(2,25)), using
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- Reed–Solomon code RS(22,25) [i]
- discarding factors / shortening the dual code based on linear OA(253, 25, F25, 3) (dual of [25, 22, 4]-code or 25-arc in PG(2,25) or 25-cap in PG(2,25)), using
- construction X applied to C([0,11]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2592, 390645, F25, 23) (dual of [390645, 390553, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(2592, 390644, F25, 23) (dual of [390644, 390552, 24]-code), using
- net defined by OOA [i] based on linear OOA(2592, 35513, F25, 23, 23) (dual of [(35513, 23), 816707, 24]-NRT-code), using
(71, 94, 390652)-Net over F25 — Digital
Digital (71, 94, 390652)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2594, 390652, F25, 23) (dual of [390652, 390558, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,8]) [i] based on
- linear OA(2589, 390626, F25, 23) (dual of [390626, 390537, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(2565, 390626, F25, 17) (dual of [390626, 390561, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 390626 | 258−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (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([0,11]) ⊂ C([0,8]) [i] based on
(71, 94, large)-Net in Base 25 — Upper bound on s
There is no (71, 94, large)-net in base 25, because
- 21 times m-reduction [i] would yield (71, 73, large)-net in base 25, but