MinT - Best Known (54−16, 54, s)-Nets in Base 2

Best Known (54−16, 54, s)-Nets in Base 2

(54−16, 54, 55)-Net over F₂ — Constructive and digital

Digital (38, 54, 55)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (6, 14, 15)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (24, 40, 40)-net over F₂, using
  - a shift-net [i]

(54−16, 54, 70)-Net over F₂ — Digital

Digital (38, 54, 70)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(54−16, 54, 393)-Net in Base 2 — Upper bound on s

There is no (38, 54, 394)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 18079 403841 255385 > 2⁵⁴ [i]