MinT - Best Known (54, 54+17, s)-Nets in Base 2

Best Known (54, 54+17, s)-Nets in Base 2

(54, 54+17, 90)-Net over F₂ — Constructive and digital

Digital (54, 71, 90)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (18, 26, 49)-net over F₂, using
  - a net from the Salzburg tables [i]
2. digital (28, 45, 45)-net over F₂, using
  - a shift-net [i]

(54, 54+17, 146)-Net over F₂ — Digital

Digital (54, 71, 146)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 54+17, 1609)-Net in Base 2 — Upper bound on s

There is no (54, 71, 1610)-net in base 2, because

1 times m-reduction [i] would yield (54, 70, 1610)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1185 053349 680686 151393 > 2⁷⁰ [i]