Best Known (62−15, 62, s)-Nets in Base 2
(62−15, 62, 90)-Net over F2 — Constructive and digital
Digital (47, 62, 90)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (12, 19, 47)-net over F2, using
- digital (28, 43, 45)-net over F2, using
- 2 times m-reduction [i] based on digital (28, 45, 45)-net over F2, using
(62−15, 62, 139)-Net over F2 — Digital
Digital (47, 62, 139)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(262, 139, F2, 2, 15) (dual of [(139, 2), 216, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(262, 278, F2, 15) (dual of [278, 216, 16]-code), using
(62−15, 62, 1409)-Net in Base 2 — Upper bound on s
There is no (47, 62, 1410)-net in base 2, because
- 1 times m-reduction [i] would yield (47, 61, 1410)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 2 309520 154234 686848 > 261 [i]