Best Known (48−6, 48, s)-Nets in Base 2
(48−6, 48, 32766)-Net over F2 — Constructive and digital
Digital (42, 48, 32766)-net over F2, using
- 21 times duplication [i] based on digital (41, 47, 32766)-net over F2, using
- net defined by OOA [i] based on linear OOA(247, 32766, F2, 6, 6) (dual of [(32766, 6), 196549, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(247, 32767, F2, 3, 6) (dual of [(32767, 3), 98254, 7]-NRT-code), using
- strength reduction [i] based on linear OOA(247, 32767, F2, 3, 7) (dual of [(32767, 3), 98254, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(247, 32767, F2, 3, 6) (dual of [(32767, 3), 98254, 7]-NRT-code), using
- net defined by OOA [i] based on linear OOA(247, 32766, F2, 6, 6) (dual of [(32766, 6), 196549, 7]-NRT-code), using
(48−6, 48, 32768)-Net over F2 — Digital
Digital (42, 48, 32768)-net over F2, using
- net defined by OOA [i] based on linear OOA(248, 32768, F2, 6, 6) (dual of [(32768, 6), 196560, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(248, 32768, F2, 5, 6) (dual of [(32768, 5), 163792, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(248, 32768, F2, 2, 6) (dual of [(32768, 2), 65488, 7]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(246, 32767, F2, 2, 6) (dual of [(32767, 2), 65488, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(248, 32768, F2, 2, 6) (dual of [(32768, 2), 65488, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(248, 32768, F2, 5, 6) (dual of [(32768, 5), 163792, 7]-NRT-code), using
(48−6, 48, 119082)-Net in Base 2 — Upper bound on s
There is no (42, 48, 119083)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 281 476286 921478 > 248 [i]