Best Known (131−10, 131, s)-Nets in Base 2
(131−10, 131, 1677849)-Net over F2 — Constructive and digital
Digital (121, 131, 1677849)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (11, 16, 129)-net over F2, using
- digital (105, 115, 1677720)-net over F2, using
- net defined by OOA [i] based on linear OOA(2115, 1677720, F2, 10, 10) (dual of [(1677720, 10), 16777085, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(2115, 8388600, F2, 10) (dual of [8388600, 8388485, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(2115, large, F2, 10) (dual of [large, large−115, 11]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(2115, large, F2, 10) (dual of [large, large−115, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(2115, 8388600, F2, 10) (dual of [8388600, 8388485, 11]-code), using
- net defined by OOA [i] based on linear OOA(2115, 1677720, F2, 10, 10) (dual of [(1677720, 10), 16777085, 11]-NRT-code), using
(131−10, 131, 2796330)-Net over F2 — Digital
Digital (121, 131, 2796330)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2131, 2796330, F2, 3, 10) (dual of [(2796330, 3), 8388859, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(216, 129, F2, 3, 5) (dual of [(129, 3), 371, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (11, 16, 129)-net over F2, using
- linear OOA(2115, 2796201, F2, 3, 10) (dual of [(2796201, 3), 8388488, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2115, large, F2, 10) (dual of [large, large−115, 11]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 3-folding [i] based on linear OA(2115, large, F2, 10) (dual of [large, large−115, 11]-code), using
- linear OOA(216, 129, F2, 3, 5) (dual of [(129, 3), 371, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
(131−10, 131, large)-Net in Base 2 — Upper bound on s
There is no (121, 131, large)-net in base 2, because
- 8 times m-reduction [i] would yield (121, 123, large)-net in base 2, but