Best Known (216, 241, s)-Nets in Base 2
(216, 241, 87381)-Net over F2 — Constructive and digital
Digital (216, 241, 87381)-net over F2, using
- net defined by OOA [i] based on linear OOA(2241, 87381, F2, 25, 25) (dual of [(87381, 25), 2184284, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2241, 1048573, F2, 25) (dual of [1048573, 1048332, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2241, 1048576, F2, 25) (dual of [1048576, 1048335, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(2241, 1048576, F2, 25) (dual of [1048576, 1048335, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(2241, 1048573, F2, 25) (dual of [1048573, 1048332, 26]-code), using
(216, 241, 131072)-Net over F2 — Digital
Digital (216, 241, 131072)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2241, 131072, F2, 8, 25) (dual of [(131072, 8), 1048335, 26]-NRT-code), using
- OOA 8-folding [i] based on linear OA(2241, 1048576, F2, 25) (dual of [1048576, 1048335, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 220−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- OOA 8-folding [i] based on linear OA(2241, 1048576, F2, 25) (dual of [1048576, 1048335, 26]-code), using
(216, 241, 5545745)-Net in Base 2 — Upper bound on s
There is no (216, 241, 5545746)-net in base 2, because
- 1 times m-reduction [i] would yield (216, 240, 5545746)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 766847 949477 843396 825116 965733 923640 522089 726646 466424 888754 365272 821964 > 2240 [i]