MinT - Best Known (78, 132, s)-Nets in Base 2

Best Known (78, 132, s)-Nets in Base 2

(78, 132, 56)-Net over F₂ — Constructive and digital

Digital (78, 132, 56)-net over F₂, using

trace code for nets [i] based on digital (12, 66, 28)-net over F₄, using
- net from sequence [i] based on digital (12, 27)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(78, 132, 63)-Net over F₂ — Digital

Digital (78, 132, 63)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 132, 285)-Net in Base 2 — Upper bound on s

There is no (78, 132, 286)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5542 254660 555310 052729 085351 097403 558742 > 2¹³² [i]