MinT - Best Known (42, 42+17, s)-Nets in Base 2

Best Known (42, 42+17, s)-Nets in Base 2

(42, 42+17, 60)-Net over F₂ — Constructive and digital

Digital (42, 59, 60)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 15, 16)-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]

(42, 42+17, 79)-Net over F₂ — Digital

Digital (42, 59, 79)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+17, 561)-Net in Base 2 — Upper bound on s

There is no (42, 59, 562)-net in base 2, because

1 times m-reduction [i] would yield (42, 58, 562)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 289823 436202 221650 > 2⁵⁸ [i]