Best Known (48−17, 48, s)-Nets in Base 256
(48−17, 48, 16384)-Net over F256 — Constructive and digital
Digital (31, 48, 16384)-net over F256, using
- net defined by OOA [i] based on linear OOA(25648, 16384, F256, 17, 17) (dual of [(16384, 17), 278480, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25648, 131073, F256, 17) (dual of [131073, 131025, 18]-code), using
- (u, u+v)-construction [i] based on
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using
- an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using
- (u, u+v)-construction [i] based on
- OOA 8-folding and stacking with additional row [i] based on linear OA(25648, 131073, F256, 17) (dual of [131073, 131025, 18]-code), using
(48−17, 48, 447431)-Net over F256 — Digital
Digital (31, 48, 447431)-net over F256, using
(48−17, 48, large)-Net in Base 256 — Upper bound on s
There is no (31, 48, large)-net in base 256, because
- 15 times m-reduction [i] would yield (31, 33, large)-net in base 256, but