Best Known (230−20, 230, s)-Nets in Base 2
(230−20, 230, 838860)-Net over F2 — Constructive and digital
Digital (210, 230, 838860)-net over F2, using
- net defined by OOA [i] based on linear OOA(2230, 838860, F2, 20, 20) (dual of [(838860, 20), 16776970, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(2230, 8388600, F2, 20) (dual of [8388600, 8388370, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2230, large, F2, 20) (dual of [large, large−230, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(2230, large, F2, 20) (dual of [large, large−230, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(2230, 8388600, F2, 20) (dual of [8388600, 8388370, 21]-code), using
(230−20, 230, 1198371)-Net over F2 — Digital
Digital (210, 230, 1198371)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2230, 1198371, F2, 7, 20) (dual of [(1198371, 7), 8388367, 21]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2230, 8388597, F2, 20) (dual of [8388597, 8388367, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(2230, large, F2, 20) (dual of [large, large−230, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(2230, large, F2, 20) (dual of [large, large−230, 21]-code), using
- OOA 7-folding [i] based on linear OA(2230, 8388597, F2, 20) (dual of [8388597, 8388367, 21]-code), using
(230−20, 230, large)-Net in Base 2 — Upper bound on s
There is no (210, 230, large)-net in base 2, because
- 18 times m-reduction [i] would yield (210, 212, large)-net in base 2, but