Best Known (81−24, 81, s)-Nets in Base 25
(81−24, 81, 1305)-Net over F25 — Constructive and digital
Digital (57, 81, 1305)-net over F25, using
- net defined by OOA [i] based on linear OOA(2581, 1305, F25, 24, 24) (dual of [(1305, 24), 31239, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2581, 15660, F25, 24) (dual of [15660, 15579, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2581, 15663, F25, 24) (dual of [15663, 15582, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(14) [i] based on
- linear OA(2570, 15625, F25, 24) (dual of [15625, 15555, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(2543, 15625, F25, 15) (dual of [15625, 15582, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(2511, 38, F25, 8) (dual of [38, 27, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(2511, 52, F25, 8) (dual of [52, 41, 9]-code), using
- extended algebraic-geometric code AGe(F,43P) [i] based on function field F/F25 with g(F) = 3 and N(F) ≥ 52, using
- discarding factors / shortening the dual code based on linear OA(2511, 52, F25, 8) (dual of [52, 41, 9]-code), using
- construction X applied to Ce(23) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(2581, 15663, F25, 24) (dual of [15663, 15582, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2581, 15660, F25, 24) (dual of [15660, 15579, 25]-code), using
(81−24, 81, 32929)-Net over F25 — Digital
Digital (57, 81, 32929)-net over F25, using
(81−24, 81, large)-Net in Base 25 — Upper bound on s
There is no (57, 81, large)-net in base 25, because
- 22 times m-reduction [i] would yield (57, 59, large)-net in base 25, but