MinT - Best Known (58−17, 58, s)-Nets in Base 2

Best Known (58−17, 58, s)-Nets in Base 2

(58−17, 58, 59)-Net over F₂ — Constructive and digital

Digital (41, 58, 59)-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 (27, 44, 44)-net over F₂, using
  - a shift-net [i]

(58−17, 58, 75)-Net over F₂ — Digital

Digital (41, 58, 75)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(58−17, 58, 514)-Net in Base 2 — Upper bound on s

There is no (41, 58, 515)-net in base 2, because

1 times m-reduction [i] would yield (41, 57, 515)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 146197 293392 586944 > 2⁵⁷ [i]