MinT - Best Known (59−20, 59, s)-Nets in Base 2

Best Known (59−20, 59, s)-Nets in Base 2

(59−20, 59, 44)-Net over F₂ — Constructive and digital

Digital (39, 59, 44)-net over F₂, using

1 times m-reduction [i] based on digital (39, 60, 44)-net over F₂, using
- trace code for nets [i] based on digital (9, 30, 22)-net over F₄, using
  - net from sequence [i] based on digital (9, 21)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 22, using
      - an explicitly constructive algebraic function field [i]

(59−20, 59, 54)-Net over F₂ — Digital

Digital (39, 59, 54)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(59−20, 59, 256)-Net in Base 2 — Upper bound on s

There is no (39, 59, 257)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 592283 006894 930688 > 2⁵⁹ [i]