Best Known (69, 69+30, s)-Nets in Base 25
(69, 69+30, 1044)-Net over F25 — Constructive and digital
Digital (69, 99, 1044)-net over F25, using
- 1 times m-reduction [i] based on digital (69, 100, 1044)-net over F25, using
- net defined by OOA [i] based on linear OOA(25100, 1044, F25, 31, 31) (dual of [(1044, 31), 32264, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(25100, 15661, F25, 31) (dual of [15661, 15561, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(25100, 15664, F25, 31) (dual of [15664, 15564, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(20) [i] based on
- linear OA(2588, 15625, F25, 31) (dual of [15625, 15537, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(2512, 39, F25, 9) (dual of [39, 27, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(2512, 52, F25, 9) (dual of [52, 40, 10]-code), using
- extended algebraic-geometric code AGe(F,42P) [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(2512, 52, F25, 9) (dual of [52, 40, 10]-code), using
- construction X applied to Ce(30) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(25100, 15664, F25, 31) (dual of [15664, 15564, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(25100, 15661, F25, 31) (dual of [15661, 15561, 32]-code), using
- net defined by OOA [i] based on linear OOA(25100, 1044, F25, 31, 31) (dual of [(1044, 31), 32264, 32]-NRT-code), using
(69, 69+30, 28801)-Net over F25 — Digital
Digital (69, 99, 28801)-net over F25, using
(69, 69+30, large)-Net in Base 25 — Upper bound on s
There is no (69, 99, large)-net in base 25, because
- 28 times m-reduction [i] would yield (69, 71, large)-net in base 25, but