Best Known (53−18, 53, s)-Nets in Base 256
(53−18, 53, 932067)-Net over F256 — Constructive and digital
Digital (35, 53, 932067)-net over F256, using
- 2561 times duplication [i] based on digital (34, 52, 932067)-net over F256, using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- net defined by OOA [i] based on linear OOA(25652, 932067, F256, 18, 18) (dual of [(932067, 18), 16777154, 19]-NRT-code), using
(53−18, 53, 3883664)-Net over F256 — Digital
Digital (35, 53, 3883664)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25653, 3883664, F256, 2, 18) (dual of [(3883664, 2), 7767275, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25653, 4194301, F256, 2, 18) (dual of [(4194301, 2), 8388549, 19]-NRT-code), using
- 2561 times duplication [i] based on linear OOA(25652, 4194301, F256, 2, 18) (dual of [(4194301, 2), 8388550, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25652, 8388602, F256, 18) (dual of [8388602, 8388550, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(25652, large, F256, 18) (dual of [large, large−52, 19]-code), using
- OOA 2-folding [i] based on linear OA(25652, 8388602, F256, 18) (dual of [8388602, 8388550, 19]-code), using
- 2561 times duplication [i] based on linear OOA(25652, 4194301, F256, 2, 18) (dual of [(4194301, 2), 8388550, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(25653, 4194301, F256, 2, 18) (dual of [(4194301, 2), 8388549, 19]-NRT-code), using
(53−18, 53, large)-Net in Base 256 — Upper bound on s
There is no (35, 53, large)-net in base 256, because
- 16 times m-reduction [i] would yield (35, 37, large)-net in base 256, but