Best Known (240−24, 240, s)-Nets in Base 2
(240−24, 240, 87381)-Net over F2 — Constructive and digital
Digital (216, 240, 87381)-net over F2, using
- net defined by OOA [i] based on linear OOA(2240, 87381, F2, 24, 24) (dual of [(87381, 24), 2096904, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2240, 1048572, F2, 24) (dual of [1048572, 1048332, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2240, 1048576, F2, 24) (dual of [1048576, 1048336, 25]-code), using
- 1 times truncation [i] based on linear OA(2241, 1048577, F2, 25) (dual of [1048577, 1048336, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2241, 1048577, F2, 25) (dual of [1048577, 1048336, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2240, 1048576, F2, 24) (dual of [1048576, 1048336, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2240, 1048572, F2, 24) (dual of [1048572, 1048332, 25]-code), using
(240−24, 240, 149796)-Net over F2 — Digital
Digital (216, 240, 149796)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2240, 149796, F2, 7, 24) (dual of [(149796, 7), 1048332, 25]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2240, 1048572, F2, 24) (dual of [1048572, 1048332, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2240, 1048576, F2, 24) (dual of [1048576, 1048336, 25]-code), using
- 1 times truncation [i] based on linear OA(2241, 1048577, F2, 25) (dual of [1048577, 1048336, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 1048577 | 240−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2241, 1048577, F2, 25) (dual of [1048577, 1048336, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2240, 1048576, F2, 24) (dual of [1048576, 1048336, 25]-code), using
- OOA 7-folding [i] based on linear OA(2240, 1048572, F2, 24) (dual of [1048572, 1048332, 25]-code), using
(240−24, 240, 5545745)-Net in Base 2 — Upper bound on s
There is no (216, 240, 5545746)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 766847 949477 843396 825116 965733 923640 522089 726646 466424 888754 365272 821964 > 2240 [i]