MinT - Best Known (211−61, 211, s)-Nets in Base 2

Best Known (211−61, 211, s)-Nets in Base 2

(211−61, 211, 135)-Net over F₂ — Constructive and digital

Digital (150, 211, 135)-net over F₂, using

2¹ times duplication [i] based on digital (149, 210, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 70, 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]

(211−61, 211, 204)-Net over F₂ — Digital

Digital (150, 211, 204)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(211−61, 211, 1497)-Net in Base 2 — Upper bound on s

There is no (150, 211, 1498)-net in base 2, because

1 times m-reduction [i] would yield (150, 210, 1498)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1652 750448 200142 513204 161508 235608 986461 129672 817286 767861 658336 > 2²¹⁰ [i]