MinT - Best Known (55−14, 55, s)-Nets in Base 2

Best Known (55−14, 55, s)-Nets in Base 2

(55−14, 55, 76)-Net over F₂ — Constructive and digital

Digital (41, 55, 76)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (11, 18, 41)-net over F₂, using
  - linear code embedding found in a computer search [i]
2. digital (23, 37, 38)-net over F₂, using
  - 1 times m-reduction [i] based on digital (23, 38, 38)-net over F₂, using
    - a shift-net [i]

(55−14, 55, 106)-Net over F₂ — Digital

Digital (41, 55, 106)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(55−14, 55, 773)-Net in Base 2 — Upper bound on s

There is no (41, 55, 774)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 36104 852052 494764 > 2⁵⁵ [i]