Best Known (33−6, 33, s)-Nets in Base 2
(33−6, 33, 1022)-Net over F2 — Constructive and digital
Digital (27, 33, 1022)-net over F2, using
- 21 times duplication [i] based on digital (26, 32, 1022)-net over F2, using
- net defined by OOA [i] based on linear OOA(232, 1022, F2, 6, 6) (dual of [(1022, 6), 6100, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(232, 1023, F2, 3, 6) (dual of [(1023, 3), 3037, 7]-NRT-code), using
- strength reduction [i] based on linear OOA(232, 1023, F2, 3, 7) (dual of [(1023, 3), 3037, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(232, 1023, F2, 3, 6) (dual of [(1023, 3), 3037, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(232, 1022, F2, 6, 6) (dual of [(1022, 6), 6100, 7]-NRT-code), using
(33−6, 33, 1024)-Net over F2 — Digital
Digital (27, 33, 1024)-net over F2, using
- net defined by OOA [i] based on linear OOA(233, 1024, F2, 6, 6) (dual of [(1024, 6), 6111, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(233, 1024, F2, 5, 6) (dual of [(1024, 5), 5087, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(233, 1024, F2, 2, 6) (dual of [(1024, 2), 2015, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(231, 1023, F2, 2, 6) (dual of [(1023, 2), 2015, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(233, 1024, F2, 2, 6) (dual of [(1024, 2), 2015, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(233, 1024, F2, 5, 6) (dual of [(1024, 5), 5087, 7]-NRT-code), using
(33−6, 33, 3717)-Net in Base 2 — Upper bound on s
There is no (27, 33, 3718)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 8593 642058 > 233 [i]