Best Known (92−28, 92, s)-Nets in Base 25
(92−28, 92, 1119)-Net over F25 — Constructive and digital
Digital (64, 92, 1119)-net over F25, using
- net defined by OOA [i] based on linear OOA(2592, 1119, F25, 28, 28) (dual of [(1119, 28), 31240, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(2592, 15666, F25, 28) (dual of [15666, 15574, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2592, 15668, F25, 28) (dual of [15668, 15576, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(16) [i] based on
- linear OA(2579, 15625, F25, 28) (dual of [15625, 15546, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2549, 15625, F25, 17) (dual of [15625, 15576, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2513, 43, F25, 10) (dual of [43, 30, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2513, 52, F25, 10) (dual of [52, 39, 11]-code), using
- extended algebraic-geometric code AGe(F,41P) [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(2513, 52, F25, 10) (dual of [52, 39, 11]-code), using
- construction X applied to Ce(27) ⊂ Ce(16) [i] based on
- discarding factors / shortening the dual code based on linear OA(2592, 15668, F25, 28) (dual of [15668, 15576, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(2592, 15666, F25, 28) (dual of [15666, 15574, 29]-code), using
(92−28, 92, 26410)-Net over F25 — Digital
Digital (64, 92, 26410)-net over F25, using
(92−28, 92, large)-Net in Base 25 — Upper bound on s
There is no (64, 92, large)-net in base 25, because
- 26 times m-reduction [i] would yield (64, 66, large)-net in base 25, but