Best Known (28−10, 28, s)-Nets in Base 2
(28−10, 28, 32)-Net over F2 — Constructive and digital
Digital (18, 28, 32)-net over F2, using
- 4 times m-reduction [i] based on digital (18, 32, 32)-net over F2, using
(28−10, 28, 34)-Net over F2 — Digital
Digital (18, 28, 34)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(228, 34, F2, 2, 10) (dual of [(34, 2), 40, 11]-NRT-code), using
- OOA 2-folding [i] based on linear OA(228, 68, F2, 10) (dual of [68, 40, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(228, 69, F2, 10) (dual of [69, 41, 11]-code), using
- a “Gra†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(228, 69, F2, 10) (dual of [69, 41, 11]-code), using
- OOA 2-folding [i] based on linear OA(228, 68, F2, 10) (dual of [68, 40, 11]-code), using
(28−10, 28, 119)-Net in Base 2 — Upper bound on s
There is no (18, 28, 120)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 273 568775 > 228 [i]