Best Known (115, 115+10, s)-Nets in Base 2
(115, 115+10, 1677740)-Net over F2 — Constructive and digital
Digital (115, 125, 1677740)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (5, 10, 20)-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
(115, 115+10, 2796221)-Net over F2 — Digital
Digital (115, 125, 2796221)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2125, 2796221, F2, 3, 10) (dual of [(2796221, 3), 8388538, 11]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(210, 20, F2, 3, 5) (dual of [(20, 3), 50, 6]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 10, 20)-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(210, 20, F2, 3, 5) (dual of [(20, 3), 50, 6]-NRT-code), using
- (u, u+v)-construction [i] based on
(115, 115+10, large)-Net in Base 2 — Upper bound on s
There is no (115, 125, large)-net in base 2, because
- 8 times m-reduction [i] would yield (115, 117, large)-net in base 2, but