Best Known (17, 27, s)-Nets in Base 2
(17, 27, 30)-Net over F2 — Constructive and digital
Digital (17, 27, 30)-net over F2, using
- 3 times m-reduction [i] based on digital (17, 30, 30)-net over F2, using
(17, 27, 31)-Net over F2 — Digital
Digital (17, 27, 31)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(227, 31, F2, 2, 10) (dual of [(31, 2), 35, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(227, 62, F2, 10) (dual of [62, 35, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(227, 63, F2, 10) (dual of [63, 36, 11]-code), using
- the primitive narrow-sense BCH-code C(I) with length 63 = 26−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(227, 63, F2, 10) (dual of [63, 36, 11]-code), using
- OOA 2-folding [i] based on linear OA(227, 62, F2, 10) (dual of [62, 35, 11]-code), using
(17, 27, 103)-Net in Base 2 — Upper bound on s
There is no (17, 27, 104)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 139 256547 > 227 [i]