Best Known (46, 46+24, s)-Nets in Base 25
(46, 46+24, 1302)-Net over F25 — Constructive and digital
Digital (46, 70, 1302)-net over F25, using
- net defined by OOA [i] based on linear OOA(2570, 1302, F25, 24, 24) (dual of [(1302, 24), 31178, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2570, 15624, F25, 24) (dual of [15624, 15554, 25]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2570, 15625, F25, 24) (dual of [15625, 15555, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2570, 15624, F25, 24) (dual of [15624, 15554, 25]-code), using
(46, 46+24, 9132)-Net over F25 — Digital
Digital (46, 70, 9132)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2570, 9132, F25, 24) (dual of [9132, 9062, 25]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(2570, 15625, F25, 24) (dual of [15625, 15555, 25]-code), using
(46, 46+24, large)-Net in Base 25 — Upper bound on s
There is no (46, 70, large)-net in base 25, because
- 22 times m-reduction [i] would yield (46, 48, large)-net in base 25, but