MinT - Best Known (64−17, 64, s)-Nets in Base 2

Best Known (64−17, 64, s)-Nets in Base 2

(64−17, 64, 79)-Net over F₂ — Constructive and digital

Digital (47, 64, 79)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (12, 20, 35)-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]

(64−17, 64, 102)-Net over F₂ — Digital

Digital (47, 64, 102)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(64−17, 64, 872)-Net in Base 2 — Upper bound on s

There is no (47, 64, 873)-net in base 2, because

1 times m-reduction [i] would yield (47, 63, 873)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 9 285460 852269 749413 > 2⁶³ [i]