MinT - Best Known (32−10, 32, s)-Nets in Base 2

Best Known (32−10, 32, s)-Nets in Base 2

(32−10, 32, 46)-Net over F₂ — Constructive and digital

Digital (22, 32, 46)-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, 21, 23)-net over F₂, using
  - linear code embedding found in a computer search [i]

(32−10, 32, 47)-Net over F₂ — Digital

Digital (22, 32, 47)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(32−10, 32, 213)-Net in Base 2 — Upper bound on s

There is no (22, 32, 214)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4383 870679 > 2³² [i]