Best Known (60−21, 60, s)-Nets in Base 256
(60−21, 60, 13107)-Net over F256 — Constructive and digital
Digital (39, 60, 13107)-net over F256, using
- net defined by OOA [i] based on linear OOA(25660, 13107, F256, 21, 21) (dual of [(13107, 21), 275187, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25660, 131071, F256, 21) (dual of [131071, 131011, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(25660, 131073, F256, 21) (dual of [131073, 131013, 22]-code), using
- (u, u+v)-construction [i] based on
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using
- an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(25641, 65537, F256, 21) (dual of [65537, 65496, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,10], and minimum distance d ≥ |{−10,−9,…,10}|+1 = 22 (BCH-bound) [i]
- linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(25660, 131073, F256, 21) (dual of [131073, 131013, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(25660, 131071, F256, 21) (dual of [131071, 131011, 22]-code), using
(60−21, 60, 546379)-Net over F256 — Digital
Digital (39, 60, 546379)-net over F256, using
(60−21, 60, large)-Net in Base 256 — Upper bound on s
There is no (39, 60, large)-net in base 256, because
- 19 times m-reduction [i] would yield (39, 41, large)-net in base 256, but