Best Known (64, 64+20, s)-Nets in Base 25
(64, 64+20, 39065)-Net over F25 — Constructive and digital
Digital (64, 84, 39065)-net over F25, using
- 252 times duplication [i] based on digital (62, 82, 39065)-net over F25, using
- net defined by OOA [i] based on linear OOA(2582, 39065, F25, 20, 20) (dual of [(39065, 20), 781218, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2582, 390650, F25, 20) (dual of [390650, 390568, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2582, 390651, F25, 20) (dual of [390651, 390569, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(13) [i] based on
- linear OA(2577, 390625, F25, 20) (dual of [390625, 390548, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2553, 390625, F25, 14) (dual of [390625, 390572, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 390624 = 254−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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 Ce(19) ⊂ Ce(13) [i] based on
- discarding factors / shortening the dual code based on linear OA(2582, 390651, F25, 20) (dual of [390651, 390569, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2582, 390650, F25, 20) (dual of [390650, 390568, 21]-code), using
- net defined by OOA [i] based on linear OOA(2582, 39065, F25, 20, 20) (dual of [(39065, 20), 781218, 21]-NRT-code), using
(64, 64+20, 500471)-Net over F25 — Digital
Digital (64, 84, 500471)-net over F25, using
(64, 64+20, large)-Net in Base 25 — Upper bound on s
There is no (64, 84, large)-net in base 25, because
- 18 times m-reduction [i] would yield (64, 66, large)-net in base 25, but