Best Known (24, 24+13, s)-Nets in Base 25
(24, 24+13, 2604)-Net over F25 — Constructive and digital
Digital (24, 37, 2604)-net over F25, using
- net defined by OOA [i] based on linear OOA(2537, 2604, F25, 13, 13) (dual of [(2604, 13), 33815, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(2537, 15625, F25, 13) (dual of [15625, 15588, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 6-folding and stacking with additional row [i] based on linear OA(2537, 15625, F25, 13) (dual of [15625, 15588, 14]-code), using
(24, 24+13, 7814)-Net over F25 — Digital
Digital (24, 37, 7814)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2537, 7814, F25, 2, 13) (dual of [(7814, 2), 15591, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2537, 15628, F25, 13) (dual of [15628, 15591, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- linear OA(2537, 15625, F25, 13) (dual of [15625, 15588, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2534, 15625, F25, 12) (dual of [15625, 15591, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(250, 3, F25, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(12) ⊂ Ce(11) [i] based on
- OOA 2-folding [i] based on linear OA(2537, 15628, F25, 13) (dual of [15628, 15591, 14]-code), using
(24, 24+13, large)-Net in Base 25 — Upper bound on s
There is no (24, 37, large)-net in base 25, because
- 11 times m-reduction [i] would yield (24, 26, large)-net in base 25, but