Best Known (39−11, 39, s)-Nets in Base 2
(39−11, 39, 58)-Net over F2 — Constructive and digital
Digital (28, 39, 58)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (7, 12, 36)-net over F2, using
- digital (16, 27, 29)-net over F2, using
- 2 times m-reduction [i] based on digital (16, 29, 29)-net over F2, using
(39−11, 39, 80)-Net over F2 — Digital
Digital (28, 39, 80)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(239, 80, F2, 2, 11) (dual of [(80, 2), 121, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(239, 160, F2, 11) (dual of [160, 121, 12]-code), using
- a “Gra†code from Grassl’s database [i]
- OOA 2-folding [i] based on linear OA(239, 160, F2, 11) (dual of [160, 121, 12]-code), using
(39−11, 39, 498)-Net in Base 2 — Upper bound on s
There is no (28, 39, 499)-net in base 2, because
- 1 times m-reduction [i] would yield (28, 38, 499)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 276308 478096 > 238 [i]