Best Known (67, 67+36, s)-Nets in Base 25
(67, 67+36, 868)-Net over F25 — Constructive and digital
Digital (67, 103, 868)-net over F25, using
- net defined by OOA [i] based on linear OOA(25103, 868, F25, 36, 36) (dual of [(868, 36), 31145, 37]-NRT-code), using
- OA 18-folding and stacking [i] based on linear OA(25103, 15624, F25, 36) (dual of [15624, 15521, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(25103, 15625, F25, 36) (dual of [15625, 15522, 37]-code), using
- an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- discarding factors / shortening the dual code based on linear OA(25103, 15625, F25, 36) (dual of [15625, 15522, 37]-code), using
- OA 18-folding and stacking [i] based on linear OA(25103, 15624, F25, 36) (dual of [15624, 15521, 37]-code), using
(67, 67+36, 8795)-Net over F25 — Digital
Digital (67, 103, 8795)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25103, 8795, F25, 36) (dual of [8795, 8692, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(25103, 15625, F25, 36) (dual of [15625, 15522, 37]-code), using
- an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 15624 = 253−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- discarding factors / shortening the dual code based on linear OA(25103, 15625, F25, 36) (dual of [15625, 15522, 37]-code), using
(67, 67+36, large)-Net in Base 25 — Upper bound on s
There is no (67, 103, large)-net in base 25, because
- 34 times m-reduction [i] would yield (67, 69, large)-net in base 25, but