MinT - Best Known (53, 53+17, s)-Nets in Base 2

Best Known (53, 53+17, s)-Nets in Base 2

(53, 53+17, 89)-Net over F₂ — Constructive and digital

Digital (53, 70, 89)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (17, 25, 44)-net over F₂, using
  - a net from the Salzburg tables [i]
2. digital (28, 45, 45)-net over F₂, using
  - a shift-net [i]

(53, 53+17, 139)-Net over F₂ — Digital

Digital (53, 70, 139)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+17, 1474)-Net in Base 2 — Upper bound on s

There is no (53, 70, 1475)-net in base 2, because

1 times m-reduction [i] would yield (53, 69, 1475)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 591 162608 104132 790696 > 2⁶⁹ [i]