MinT - Best Known (206−59, 206, s)-Nets in Base 2

Best Known (206−59, 206, s)-Nets in Base 2

(206−59, 206, 135)-Net over F₂ — Constructive and digital

Digital (147, 206, 135)-net over F₂, using

1 times m-reduction [i] based on digital (147, 207, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 69, 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]

(206−59, 206, 204)-Net over F₂ — Digital

Digital (147, 206, 204)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(206−59, 206, 1524)-Net in Base 2 — Upper bound on s

There is no (147, 206, 1525)-net in base 2, because

1 times m-reduction [i] would yield (147, 205, 1525)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 51 787577 103928 069718 094818 014299 257748 289231 577097 807001 785112 > 2²⁰⁵ [i]