MinT - Best Known (186−78, 186, s)-Nets in Base 2

Best Known (186−78, 186, s)-Nets in Base 2

(186−78, 186, 66)-Net over F₂ — Constructive and digital

Digital (108, 186, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 93, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(186−78, 186, 78)-Net over F₂ — Digital

Digital (108, 186, 78)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−78, 186, 365)-Net in Base 2 — Upper bound on s

There is no (108, 186, 366)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 105 014887 677788 677155 148180 852055 316481 444044 226852 051104 > 2¹⁸⁶ [i]