Best Known (30−9, 30, s)-Nets in Base 256
(30−9, 30, 2097408)-Net over F256 — Constructive and digital
Digital (21, 30, 2097408)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (16, 25, 2097150)-net over F256, using
- net defined by OOA [i] based on linear OOA(25625, 2097150, F256, 9, 9) (dual of [(2097150, 9), 18874325, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(25625, 8388601, F256, 9) (dual of [8388601, 8388576, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding factors / shortening the dual code based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(25625, 8388601, F256, 9) (dual of [8388601, 8388576, 10]-code), using
- net defined by OOA [i] based on linear OOA(25625, 2097150, F256, 9, 9) (dual of [(2097150, 9), 18874325, 10]-NRT-code), using
- digital (1, 5, 258)-net over F256, using
(30−9, 30, large)-Net over F256 — Digital
Digital (21, 30, large)-net over F256, using
- 1 times m-reduction [i] based on digital (21, 31, large)-net over F256, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25631, large, F256, 10) (dual of [large, large−31, 11]-code), using
- strength reduction [i] based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- strength reduction [i] based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25631, large, F256, 10) (dual of [large, large−31, 11]-code), using
(30−9, 30, large)-Net in Base 256 — Upper bound on s
There is no (21, 30, large)-net in base 256, because
- 7 times m-reduction [i] would yield (21, 23, large)-net in base 256, but