MinT - Best Known (45, 45+16, s)-Nets in Base 2

Best Known (45, 45+16, s)-Nets in Base 2

(45, 45+16, 79)-Net over F₂ — Constructive and digital

Digital (45, 61, 79)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (13, 21, 39)-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]

(45, 45+16, 103)-Net over F₂ — Digital

Digital (45, 61, 103)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(45, 45+16, 731)-Net in Base 2 — Upper bound on s

There is no (45, 61, 732)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 313990 352850 875795 > 2⁶¹ [i]