MinT - Best Known (86, 152, s)-Nets in Base 2

Best Known (86, 152, s)-Nets in Base 2

(86, 152, 54)-Net over F₂ — Constructive and digital

Digital (86, 152, 54)-net over F₂, using

trace code for nets [i] based on digital (10, 76, 27)-net over F₄, using
- net from sequence [i] based on digital (10, 26)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]

(86, 152, 61)-Net over F₂ — Digital

Digital (86, 152, 61)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(86, 152, 274)-Net in Base 2 — Upper bound on s

There is no (86, 152, 275)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5874 969732 259923 602112 816799 840556 674982 118432 > 2¹⁵² [i]