Best Known (41−11, 41, s)-Nets in Base 2
(41−11, 41, 64)-Net over F2 — Constructive and digital
Digital (30, 41, 64)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (7, 12, 36)-net over F2, using
- digital (18, 29, 32)-net over F2, using
- 3 times m-reduction [i] based on digital (18, 32, 32)-net over F2, using
(41−11, 41, 100)-Net over F2 — Digital
Digital (30, 41, 100)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(241, 100, F2, 2, 11) (dual of [(100, 2), 159, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(241, 128, F2, 2, 11) (dual of [(128, 2), 215, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(241, 256, F2, 11) (dual of [256, 215, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 2-folding [i] based on linear OA(241, 256, F2, 11) (dual of [256, 215, 12]-code), using
- discarding factors / shortening the dual code based on linear OOA(241, 128, F2, 2, 11) (dual of [(128, 2), 215, 12]-NRT-code), using
(41−11, 41, 659)-Net in Base 2 — Upper bound on s
There is no (30, 41, 660)-net in base 2, because
- 1 times m-reduction [i] would yield (30, 40, 660)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 099881 388508 > 240 [i]