Best Known (50, 60, s)-Nets in Base 2
(50, 60, 819)-Net over F2 — Constructive and digital
Digital (50, 60, 819)-net over F2, using
- net defined by OOA [i] based on linear OOA(260, 819, F2, 10, 10) (dual of [(819, 10), 8130, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(260, 4095, F2, 10) (dual of [4095, 4035, 11]-code), using
- 1 times truncation [i] based on linear OA(261, 4096, F2, 11) (dual of [4096, 4035, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 1 times truncation [i] based on linear OA(261, 4096, F2, 11) (dual of [4096, 4035, 12]-code), using
- OA 5-folding and stacking [i] based on linear OA(260, 4095, F2, 10) (dual of [4095, 4035, 11]-code), using
(50, 60, 1365)-Net over F2 — Digital
Digital (50, 60, 1365)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(260, 1365, F2, 3, 10) (dual of [(1365, 3), 4035, 11]-NRT-code), using
- OOA 3-folding [i] based on linear OA(260, 4095, F2, 10) (dual of [4095, 4035, 11]-code), using
- 1 times truncation [i] based on linear OA(261, 4096, F2, 11) (dual of [4096, 4035, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 1 times truncation [i] based on linear OA(261, 4096, F2, 11) (dual of [4096, 4035, 12]-code), using
- OOA 3-folding [i] based on linear OA(260, 4095, F2, 10) (dual of [4095, 4035, 11]-code), using
(50, 60, 10663)-Net in Base 2 — Upper bound on s
There is no (50, 60, 10664)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1 153038 883580 615219 > 260 [i]