Best Known (69−21, 69, s)-Nets in Base 25
(69−21, 69, 1565)-Net over F25 — Constructive and digital
Digital (48, 69, 1565)-net over F25, using
- 252 times duplication [i] based on digital (46, 67, 1565)-net over F25, using
- net defined by OOA [i] based on linear OOA(2567, 1565, F25, 21, 21) (dual of [(1565, 21), 32798, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(2567, 15651, F25, 21) (dual of [15651, 15584, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(13) [i] based on
- linear OA(2561, 15625, F25, 21) (dual of [15625, 15564, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(2540, 15625, F25, 14) (dual of [15625, 15585, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [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(20) ⊂ Ce(13) [i] based on
- OOA 10-folding and stacking with additional row [i] based on linear OA(2567, 15651, F25, 21) (dual of [15651, 15584, 22]-code), using
- net defined by OOA [i] based on linear OOA(2567, 1565, F25, 21, 21) (dual of [(1565, 21), 32798, 22]-NRT-code), using
(69−21, 69, 23024)-Net over F25 — Digital
Digital (48, 69, 23024)-net over F25, using
(69−21, 69, large)-Net in Base 25 — Upper bound on s
There is no (48, 69, large)-net in base 25, because
- 19 times m-reduction [i] would yield (48, 50, large)-net in base 25, but