Best Known (17, 17+9, s)-Nets in Base 256
(17, 17+9, 2097150)-Net over F256 — Constructive and digital
Digital (17, 26, 2097150)-net over F256, using
- 2561 times duplication [i] based on 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
(17, 17+9, 5287316)-Net over F256 — Digital
Digital (17, 26, 5287316)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25626, 5287316, F256, 9) (dual of [5287316, 5287290, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(25626, large, F256, 9) (dual of [large, large−26, 10]-code), using
- 1 times code embedding in larger space [i] 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]
- 1 times code embedding in larger space [i] based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(25626, large, F256, 9) (dual of [large, large−26, 10]-code), using
(17, 17+9, large)-Net in Base 256 — Upper bound on s
There is no (17, 26, large)-net in base 256, because
- 7 times m-reduction [i] would yield (17, 19, large)-net in base 256, but