Best Known (199, 199+18, s)-Nets in Base 2
(199, 199+18, 932072)-Net over F2 — Constructive and digital
Digital (199, 217, 932072)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (1, 10, 5)-net over F2, using
- net from sequence [i] based on digital (1, 4)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (1, 4)-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 (1, 10, 5)-net over F2, using
(199, 199+18, 1398105)-Net over F2 — Digital
Digital (199, 217, 1398105)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2217, 1398105, F2, 6, 18) (dual of [(1398105, 6), 8388413, 19]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(210, 5, F2, 6, 9) (dual of [(5, 6), 20, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(6;F,20P) [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, 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(210, 5, F2, 6, 9) (dual of [(5, 6), 20, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
(199, 199+18, large)-Net in Base 2 — Upper bound on s
There is no (199, 217, large)-net in base 2, because
- 16 times m-reduction [i] would yield (199, 201, large)-net in base 2, but