Best Known (42, 42+22, s)-Nets in Base 256
(42, 42+22, 762600)-Net over F256 — Constructive and digital
Digital (42, 64, 762600)-net over F256, using
- net defined by OOA [i] based on linear OOA(25664, 762600, F256, 22, 22) (dual of [(762600, 22), 16777136, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(25664, 8388600, F256, 22) (dual of [8388600, 8388536, 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
- OA 11-folding and stacking [i] based on linear OA(25664, 8388600, F256, 22) (dual of [8388600, 8388536, 23]-code), using
(42, 42+22, 2796201)-Net over F256 — Digital
Digital (42, 64, 2796201)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(25664, 2796201, F256, 3, 22) (dual of [(2796201, 3), 8388539, 23]-NRT-code), using
- OOA 3-folding [i] 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]
- OOA 3-folding [i] based on linear OA(25664, large, F256, 22) (dual of [large, large−64, 23]-code), using
(42, 42+22, large)-Net in Base 256 — Upper bound on s
There is no (42, 64, large)-net in base 256, because
- 20 times m-reduction [i] would yield (42, 44, large)-net in base 256, but