Best Known (10, 10+6, s)-Nets in Base 256
(10, 10+6, 2796201)-Net over F256 — Constructive and digital
Digital (10, 16, 2796201)-net over F256, using
- net defined by OOA [i] based on linear OOA(25616, 2796201, F256, 6, 6) (dual of [(2796201, 6), 16777190, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
(10, 10+6, large)-Net over F256 — Digital
Digital (10, 16, large)-net over F256, using
- net defined by OOA [i] based on linear OOA(25616, large, F256, 6, 6), using
- appending kth column [i] based on linear OOA(25616, large, F256, 5, 6), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(25616, large, F256, 6) (dual of [large, large−16, 7]-code), using
- appending kth column [i] based on linear OOA(25616, large, F256, 5, 6), using
(10, 10+6, large)-Net in Base 256 — Upper bound on s
There is no (10, 16, large)-net in base 256, because
- 4 times m-reduction [i] would yield (10, 12, large)-net in base 256, but