Best Known (65−17, 65, s)-Nets in Base 2
(65−17, 65, 83)-Net over F2 — Constructive and digital
Digital (48, 65, 83)-net over F2, using
- (u, u+v)-construction [i] based on
(65−17, 65, 119)-Net over F2 — Digital
Digital (48, 65, 119)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(265, 119, F2, 2, 17) (dual of [(119, 2), 173, 18]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(265, 128, F2, 2, 17) (dual of [(128, 2), 191, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(265, 256, F2, 17) (dual of [256, 191, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 255 = 28−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 2-folding [i] based on linear OA(265, 256, F2, 17) (dual of [256, 191, 18]-code), using
- discarding factors / shortening the dual code based on linear OOA(265, 128, F2, 2, 17) (dual of [(128, 2), 191, 18]-NRT-code), using
(65−17, 65, 952)-Net in Base 2 — Upper bound on s
There is no (48, 65, 953)-net in base 2, because
- 1 times m-reduction [i] would yield (48, 64, 953)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 18 564345 698886 502091 > 264 [i]