Best Known (148−12, 148, s)-Nets in Base 2
(148−12, 148, 1398111)-Net over F2 — Constructive and digital
Digital (136, 148, 1398111)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (4, 10, 11)-net over F2, using
- 1 times m-reduction [i] based on digital (4, 11, 11)-net over F2, 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 (4, 10, 11)-net over F2, using
(148−12, 148, 2097161)-Net over F2 — Digital
Digital (136, 148, 2097161)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2148, 2097161, F2, 4, 12) (dual of [(2097161, 4), 8388496, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(210, 11, F2, 4, 6) (dual of [(11, 4), 34, 7]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 10, 11)-net over F2, using
- 1 times m-reduction [i] based on digital (4, 11, 11)-net over F2, using
- extracting embedded OOA [i] based on digital (4, 10, 11)-net over F2, using
- linear OOA(2138, 2097150, F2, 4, 12) (dual of [(2097150, 4), 8388462, 13]-NRT-code), using
- OOA 4-folding [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
- OOA 4-folding [i] based on linear OA(2138, 8388600, F2, 12) (dual of [8388600, 8388462, 13]-code), using
- linear OOA(210, 11, F2, 4, 6) (dual of [(11, 4), 34, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
(148−12, 148, large)-Net in Base 2 — Upper bound on s
There is no (136, 148, large)-net in base 2, because
- 10 times m-reduction [i] would yield (136, 138, large)-net in base 2, but