Best Known (20−7, 20, s)-Nets in Base 2
(20−7, 20, 62)-Net over F2 — Constructive and digital
Digital (13, 20, 62)-net over F2, using
- net defined by OOA [i] based on linear OOA(220, 62, F2, 7, 7) (dual of [(62, 7), 414, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(220, 63, F2, 3, 7) (dual of [(63, 3), 169, 8]-NRT-code), using
(20−7, 20, 63)-Net over F2 — Digital
Digital (13, 20, 63)-net over F2, using
- net defined by OOA [i] based on linear OOA(220, 63, F2, 7, 7) (dual of [(63, 7), 421, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(220, 63, F2, 6, 7) (dual of [(63, 6), 358, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(220, 63, F2, 3, 7) (dual of [(63, 3), 169, 8]-NRT-code), using
- appending kth column [i] based on linear OOA(220, 63, F2, 6, 7) (dual of [(63, 6), 358, 8]-NRT-code), using
(20−7, 20, 142)-Net in Base 2 — Upper bound on s
There is no (13, 20, 143)-net in base 2, because
- 1 times m-reduction [i] would yield (13, 19, 143)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 528958 > 219 [i]