MinT - Best Known (59−14, 59, s)-Nets in Base 2

Best Known (59−14, 59, s)-Nets in Base 2

(59−14, 59, 85)-Net over F₂ — Constructive and digital

Digital (45, 59, 85)-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 (27, 41, 44)-net over F₂, using
  - 3 times m-reduction [i] based on digital (27, 44, 44)-net over F₂, using
    - a shift-net [i]

(59−14, 59, 137)-Net over F₂ — Digital

Digital (45, 59, 137)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(59−14, 59, 1154)-Net in Base 2 — Upper bound on s

There is no (45, 59, 1155)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 577767 064758 115552 > 2⁵⁹ [i]