MinT - Best Known (56−16, 56, s)-Nets in Base 2

Best Known (56−16, 56, s)-Nets in Base 2

(56−16, 56, 59)-Net over F₂ — Constructive and digital

Digital (40, 56, 59)-net over F₂, using

(u,Â u+v)-construction [i] based on
1. digital (8, 16, 19)-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]

(56−16, 56, 78)-Net over F₂ — Digital

Digital (40, 56, 78)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(56−16, 56, 470)-Net in Base 2 — Upper bound on s

There is no (40, 56, 471)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 72709 806769 910818 > 2⁵⁶ [i]