MinT - Best Known (50−14, 50, s)-Nets in Base 2

Best Known (50−14, 50, s)-Nets in Base 2

(50−14, 50, 66)-Net over F₂ — Constructive and digital

Digital (36, 50, 66)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (10, 17, 34)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (19, 33, 33)-net over F₂, using
  - a shift-net [i]

(50−14, 50, 77)-Net over F₂ — Digital

Digital (36, 50, 77)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(50−14, 50, 467)-Net in Base 2 — Upper bound on s

There is no (36, 50, 468)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1129 756622 232460 > 2⁵⁰ [i]