MinT - Best Known (104−25, 104, s)-Nets in Base 2

Best Known (104−25, 104, s)-Nets in Base 2

(104−25, 104, 135)-Net over F₂ — Constructive and digital

Digital (79, 104, 135)-net over F₂, using

1 times m-reduction [i] based on digital (79, 105, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 35, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]

(104−25, 104, 185)-Net over F₂ — Digital

Digital (79, 104, 185)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(104−25, 104, 2011)-Net in Base 2 — Upper bound on s

There is no (79, 104, 2012)-net in base 2, because

1 times m-reduction [i] would yield (79, 103, 2012)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10 189619 232445 904249 047807 245444 > 2¹⁰³ [i]