Best Known (150, 150+12, s)-Nets in Base 2
(150, 150+12, 1398230)-Net over F2 — Constructive and digital
Digital (150, 162, 1398230)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (18, 24, 130)-net over F2, using
- net defined by OOA [i] based on linear OOA(224, 130, F2, 6, 6) (dual of [(130, 6), 756, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(224, 130, F2, 5, 6) (dual of [(130, 5), 626, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(23, 3, F2, 5, 3) (dual of [(3, 5), 12, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(5;12,2) [i]
- linear OOA(221, 127, F2, 5, 6) (dual of [(127, 5), 614, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 21, 127)-net over F2, using
- linear OOA(23, 3, F2, 5, 3) (dual of [(3, 5), 12, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(224, 130, F2, 5, 6) (dual of [(130, 5), 626, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(224, 130, F2, 6, 6) (dual of [(130, 6), 756, 7]-NRT-code), using
- digital (126, 138, 1398100)-net over F2, using
- net defined by OOA [i] based on linear OOA(2138, 1398100, F2, 12, 12) (dual of [(1398100, 12), 16777062, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(2138, 8388600, F2, 12) (dual of [8388600, 8388462, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(2138, 8388600, F2, 12) (dual of [8388600, 8388462, 13]-code), using
- net defined by OOA [i] based on linear OOA(2138, 1398100, F2, 12, 12) (dual of [(1398100, 12), 16777062, 13]-NRT-code), using
- digital (18, 24, 130)-net over F2, using
(150, 150+12, 2796331)-Net over F2 — Digital
Digital (150, 162, 2796331)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2162, 2796331, F2, 3, 12) (dual of [(2796331, 3), 8388831, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(224, 130, F2, 3, 6) (dual of [(130, 3), 366, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(23, 3, F2, 3, 3) (dual of [(3, 3), 6, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;6,2) [i]
- linear OOA(221, 127, F2, 3, 6) (dual of [(127, 3), 360, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (15, 21, 127)-net over F2, using
- linear OOA(23, 3, F2, 3, 3) (dual of [(3, 3), 6, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(2138, 2796201, F2, 3, 12) (dual of [(2796201, 3), 8388465, 13]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- OOA 3-folding [i] based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- linear OOA(224, 130, F2, 3, 6) (dual of [(130, 3), 366, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
(150, 150+12, large)-Net in Base 2 — Upper bound on s
There is no (150, 162, large)-net in base 2, because
- 10 times m-reduction [i] would yield (150, 152, large)-net in base 2, but