Best Known (242−20, 242, s)-Nets in Base 2
(242−20, 242, 838866)-Net over F2 — Constructive and digital
Digital (222, 242, 838866)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (2, 12, 6)-net over F2, using
- net from sequence [i] based on digital (2, 5)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 2 and N(F) ≥ 6, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (2, 5)-sequence over F2, using
- 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
- net defined by OOA [i] based on linear OOA(2230, 838860, F2, 20, 20) (dual of [(838860, 20), 16776970, 21]-NRT-code), using
- digital (2, 12, 6)-net over F2, using
(242−20, 242, 1398106)-Net over F2 — Digital
Digital (222, 242, 1398106)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2242, 1398106, F2, 6, 20) (dual of [(1398106, 6), 8388394, 21]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(212, 6, F2, 6, 10) (dual of [(6, 6), 24, 11]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(6;F,25P) [i] based on function field F/F2 with g(F) = 2 and N(F) ≥ 6, using
- linear OOA(2230, 1398100, F2, 6, 20) (dual of [(1398100, 6), 8388370, 21]-NRT-code), using
- OOA 6-folding [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
- OOA 6-folding [i] based on linear OA(2230, 8388600, F2, 20) (dual of [8388600, 8388370, 21]-code), using
- linear OOA(212, 6, F2, 6, 10) (dual of [(6, 6), 24, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
(242−20, 242, large)-Net in Base 2 — Upper bound on s
There is no (222, 242, large)-net in base 2, because
- 18 times m-reduction [i] would yield (222, 224, large)-net in base 2, but