Best Known (74−25, 74, s)-Nets in Base 25
(74−25, 74, 1302)-Net over F25 — Constructive and digital
Digital (49, 74, 1302)-net over F25, using
- 251 times duplication [i] based on digital (48, 73, 1302)-net over F25, using
- net defined by OOA [i] based on linear OOA(2573, 1302, F25, 25, 25) (dual of [(1302, 25), 32477, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2573, 15625, F25, 25) (dual of [15625, 15552, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2573, 15626, F25, 25) (dual of [15626, 15553, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2573, 15626, F25, 25) (dual of [15626, 15553, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2573, 15625, F25, 25) (dual of [15625, 15552, 26]-code), using
- net defined by OOA [i] based on linear OOA(2573, 1302, F25, 25, 25) (dual of [(1302, 25), 32477, 26]-NRT-code), using
(74−25, 74, 10733)-Net over F25 — Digital
Digital (49, 74, 10733)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2574, 10733, F25, 25) (dual of [10733, 10659, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2574, 15633, F25, 25) (dual of [15633, 15559, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- linear OA(2573, 15626, F25, 25) (dual of [15626, 15553, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(2567, 15626, F25, 23) (dual of [15626, 15559, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 15626 | 256−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(251, 7, F25, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- discarding factors / shortening the dual code based on linear OA(2574, 15633, F25, 25) (dual of [15633, 15559, 26]-code), using
(74−25, 74, large)-Net in Base 25 — Upper bound on s
There is no (49, 74, large)-net in base 25, because
- 23 times m-reduction [i] would yield (49, 51, large)-net in base 25, but