Best Known (65−20, 65, s)-Nets in Base 25
(65−20, 65, 1565)-Net over F25 — Constructive and digital
Digital (45, 65, 1565)-net over F25, using
- 251 times duplication [i] based on digital (44, 64, 1565)-net over F25, using
- net defined by OOA [i] based on linear OOA(2564, 1565, F25, 20, 20) (dual of [(1565, 20), 31236, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2564, 15650, F25, 20) (dual of [15650, 15586, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2564, 15651, F25, 20) (dual of [15651, 15587, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(12) [i] based on
- linear OA(2558, 15625, F25, 20) (dual of [15625, 15567, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(2537, 15625, F25, 13) (dual of [15625, 15588, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(256, 26, F25, 6) (dual of [26, 20, 7]-code or 26-arc in PG(5,25)), using
- extended Reed–Solomon code RSe(20,25) [i]
- algebraic-geometric code AG(F, Q+8P) with degQ = 3 and 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+5P) with degQ = 4 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(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(2564, 15651, F25, 20) (dual of [15651, 15587, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2564, 15650, F25, 20) (dual of [15650, 15586, 21]-code), using
- net defined by OOA [i] based on linear OOA(2564, 1565, F25, 20, 20) (dual of [(1565, 20), 31236, 21]-NRT-code), using
(65−20, 65, 20028)-Net over F25 — Digital
Digital (45, 65, 20028)-net over F25, using
(65−20, 65, large)-Net in Base 25 — Upper bound on s
There is no (45, 65, large)-net in base 25, because
- 18 times m-reduction [i] would yield (45, 47, large)-net in base 25, but