Best Known (128−10, 128, s)-Nets in Base 2
(128−10, 128, 1677765)-Net over F2 — Constructive and digital
Digital (118, 128, 1677765)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (8, 13, 45)-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
(128−10, 128, 2796246)-Net over F2 — Digital
Digital (118, 128, 2796246)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2128, 2796246, F2, 3, 10) (dual of [(2796246, 3), 8388610, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(213, 45, F2, 3, 5) (dual of [(45, 3), 122, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 13, 45)-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(213, 45, F2, 3, 5) (dual of [(45, 3), 122, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
(128−10, 128, large)-Net in Base 2 — Upper bound on s
There is no (118, 128, large)-net in base 2, because
- 8 times m-reduction [i] would yield (118, 120, large)-net in base 2, but