Best Known (15, 15+10, s)-Nets in Base 256
(15, 15+10, 13365)-Net over F256 — Constructive and digital
Digital (15, 25, 13365)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 6, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (9, 19, 13107)-net over F256, using
- net defined by OOA [i] based on linear OOA(25619, 13107, F256, 10, 10) (dual of [(13107, 10), 131051, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(25619, 65535, F256, 10) (dual of [65535, 65516, 11]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(25619, 65536, F256, 10) (dual of [65536, 65517, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(25619, 65535, F256, 10) (dual of [65535, 65516, 11]-code), using
- net defined by OOA [i] based on linear OOA(25619, 13107, F256, 10, 10) (dual of [(13107, 10), 131051, 11]-NRT-code), using
- digital (1, 6, 258)-net over F256, using
(15, 15+10, 79578)-Net over F256 — Digital
Digital (15, 25, 79578)-net over F256, using
(15, 15+10, large)-Net in Base 256 — Upper bound on s
There is no (15, 25, large)-net in base 256, because
- 8 times m-reduction [i] would yield (15, 17, large)-net in base 256, but