Best Known (202, 220, s)-Nets in Base 2
(202, 220, 932075)-Net over F2 — Constructive and digital
Digital (202, 220, 932075)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (4, 13, 8)-net over F2, using
- net from sequence [i] based on digital (4, 7)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 4 and N(F) ≥ 8, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (4, 7)-sequence over F2, using
- digital (189, 207, 932067)-net over F2, using
- net defined by OOA [i] based on linear OOA(2207, 932067, F2, 18, 18) (dual of [(932067, 18), 16776999, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- net defined by OOA [i] based on linear OOA(2207, 932067, F2, 18, 18) (dual of [(932067, 18), 16776999, 19]-NRT-code), using
- digital (4, 13, 8)-net over F2, using
(202, 220, 1398108)-Net over F2 — Digital
Digital (202, 220, 1398108)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2220, 1398108, F2, 6, 18) (dual of [(1398108, 6), 8388428, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(213, 8, F2, 6, 9) (dual of [(8, 6), 35, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(6;F,38P) [i] based on function field F/F2 with g(F) = 4 and N(F) ≥ 8, using
- linear OOA(2207, 1398100, F2, 6, 18) (dual of [(1398100, 6), 8388393, 19]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- OOA 6-folding [i] based on linear OA(2207, 8388600, F2, 18) (dual of [8388600, 8388393, 19]-code), using
- linear OOA(213, 8, F2, 6, 9) (dual of [(8, 6), 35, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
(202, 220, large)-Net in Base 2 — Upper bound on s
There is no (202, 220, large)-net in base 2, because
- 16 times m-reduction [i] would yield (202, 204, large)-net in base 2, but