Best Known (59−18, 59, s)-Nets in Base 25
(59−18, 59, 1739)-Net over F25 — Constructive and digital
Digital (41, 59, 1739)-net over F25, using
- 251 times duplication [i] based on digital (40, 58, 1739)-net over F25, using
- net defined by OOA [i] based on linear OOA(2558, 1739, F25, 18, 18) (dual of [(1739, 18), 31244, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2558, 15651, F25, 18) (dual of [15651, 15593, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(10) [i] based on
- linear OA(2552, 15625, F25, 18) (dual of [15625, 15573, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(2531, 15625, F25, 11) (dual of [15625, 15594, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [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(17) ⊂ Ce(10) [i] based on
- OA 9-folding and stacking [i] based on linear OA(2558, 15651, F25, 18) (dual of [15651, 15593, 19]-code), using
- net defined by OOA [i] based on linear OOA(2558, 1739, F25, 18, 18) (dual of [(1739, 18), 31244, 19]-NRT-code), using
(59−18, 59, 21261)-Net over F25 — Digital
Digital (41, 59, 21261)-net over F25, using
(59−18, 59, large)-Net in Base 25 — Upper bound on s
There is no (41, 59, large)-net in base 25, because
- 16 times m-reduction [i] would yield (41, 43, large)-net in base 25, but