MinT - Best Known (22, 22+11, s)-Nets in Base 2

Best Known (22, 22+11, s)-Nets in Base 2

(22, 22+11, 44)-Net over F₂ — Constructive and digital

Digital (22, 33, 44)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (6, 11, 26)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (11, 22, 22)-net over F₂, using
  - a shift-net [i]

(22, 22+11, 213)-Net in Base 2 — Upper bound on s

There is no (22, 33, 214)-net in base 2, because

1 times m-reduction [i] would yield (22, 32, 214)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4383 870679 > 2³² [i]