Best Known (65, 100, s)-Nets in Base 25
(65, 100, 919)-Net over F25 — Constructive and digital
Digital (65, 100, 919)-net over F25, using
- net defined by OOA [i] based on linear OOA(25100, 919, F25, 35, 35) (dual of [(919, 35), 32065, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(25100, 15624, F25, 35) (dual of [15624, 15524, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(25100, 15625, F25, 35) (dual of [15625, 15525, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(25100, 15625, F25, 35) (dual of [15625, 15525, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(25100, 15624, F25, 35) (dual of [15624, 15524, 36]-code), using
(65, 100, 8553)-Net over F25 — Digital
Digital (65, 100, 8553)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25100, 8553, F25, 35) (dual of [8553, 8453, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(25100, 15625, F25, 35) (dual of [15625, 15525, 36]-code), using
- an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [i]
- discarding factors / shortening the dual code based on linear OA(25100, 15625, F25, 35) (dual of [15625, 15525, 36]-code), using
(65, 100, large)-Net in Base 25 — Upper bound on s
There is no (65, 100, large)-net in base 25, because
- 33 times m-reduction [i] would yield (65, 67, large)-net in base 25, but