Best Known (45−10, 45, s)-Nets in Base 2
(45−10, 45, 102)-Net over F2 — Constructive and digital
Digital (35, 45, 102)-net over F2, using
- net defined by OOA [i] based on linear OOA(245, 102, F2, 10, 10) (dual of [(102, 10), 975, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(245, 510, F2, 10) (dual of [510, 465, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(245, 511, F2, 10) (dual of [511, 466, 11]-code), using
- the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(245, 511, F2, 10) (dual of [511, 466, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(245, 510, F2, 10) (dual of [510, 465, 11]-code), using
(45−10, 45, 230)-Net over F2 — Digital
Digital (35, 45, 230)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(245, 230, F2, 2, 10) (dual of [(230, 2), 415, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(245, 255, F2, 2, 10) (dual of [(255, 2), 465, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(245, 510, F2, 10) (dual of [510, 465, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(245, 511, F2, 10) (dual of [511, 466, 11]-code), using
- the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(245, 511, F2, 10) (dual of [511, 466, 11]-code), using
- OOA 2-folding [i] based on linear OA(245, 510, F2, 10) (dual of [510, 465, 11]-code), using
- discarding factors / shortening the dual code based on linear OOA(245, 255, F2, 2, 10) (dual of [(255, 2), 465, 11]-NRT-code), using
(45−10, 45, 1326)-Net in Base 2 — Upper bound on s
There is no (35, 45, 1327)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 35 202404 683452 > 245 [i]