MinT - Best Known (44−12, 44, s)-Nets in Base 2

Best Known (44−12, 44, s)-Nets in Base 2

(44−12, 44, 60)-Net over F₂ — Constructive and digital

Digital (32, 44, 60)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (9, 15, 36)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (17, 29, 30)-net over F₂, using
  - 1 times m-reduction [i] based on digital (17, 30, 30)-net over F₂, using
    - a shift-net [i]

(44−12, 44, 78)-Net over F₂ — Digital

Digital (32, 44, 78)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(44−12, 44, 474)-Net in Base 2 — Upper bound on s

There is no (32, 44, 475)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 17 729577 453646 > 2⁴⁴ [i]