Best Known (45, 45+22, s)-Nets in Base 256
(45, 45+22, 762600)-Net over F256 — Constructive and digital
Digital (45, 67, 762600)-net over F256, using
- t-expansion [i] based on digital (44, 67, 762600)-net over F256, using
- net defined by OOA [i] based on linear OOA(25667, 762600, F256, 23, 23) (dual of [(762600, 23), 17539733, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25667, 8388601, F256, 23) (dual of [8388601, 8388534, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(25667, large, F256, 23) (dual of [large, large−67, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(25667, large, F256, 23) (dual of [large, large−67, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(25667, 8388601, F256, 23) (dual of [8388601, 8388534, 24]-code), using
- net defined by OOA [i] based on linear OOA(25667, 762600, F256, 23, 23) (dual of [(762600, 23), 17539733, 24]-NRT-code), using
(45, 45+22, 4194302)-Net over F256 — Digital
Digital (45, 67, 4194302)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25667, 4194302, F256, 2, 22) (dual of [(4194302, 2), 8388537, 23]-NRT-code), using
- 2561 times duplication [i] based on linear OOA(25666, 4194302, F256, 2, 22) (dual of [(4194302, 2), 8388538, 23]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25664, 4194301, F256, 2, 22) (dual of [(4194301, 2), 8388538, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(25664, 8388602, F256, 22) (dual of [8388602, 8388538, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(25664, large, F256, 22) (dual of [large, large−64, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(25664, large, F256, 22) (dual of [large, large−64, 23]-code), using
- OOA 2-folding [i] based on linear OA(25664, 8388602, F256, 22) (dual of [8388602, 8388538, 23]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(25664, 4194301, F256, 2, 22) (dual of [(4194301, 2), 8388538, 23]-NRT-code), using
- 2561 times duplication [i] based on linear OOA(25666, 4194302, F256, 2, 22) (dual of [(4194302, 2), 8388538, 23]-NRT-code), using
(45, 45+22, large)-Net in Base 256 — Upper bound on s
There is no (45, 67, large)-net in base 256, because
- 20 times m-reduction [i] would yield (45, 47, large)-net in base 256, but