MinT - Best Known (212−61, 212, s)-Nets in Base 2

Best Known (212−61, 212, s)-Nets in Base 2

(212−61, 212, 135)-Net over F₂ — Constructive and digital

Digital (151, 212, 135)-net over F₂, using

1 times m-reduction [i] based on digital (151, 213, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 71, 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]

(212−61, 212, 207)-Net over F₂ — Digital

Digital (151, 212, 207)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−61, 212, 1533)-Net in Base 2 — Upper bound on s

There is no (151, 212, 1534)-net in base 2, because

1 times m-reduction [i] would yield (151, 211, 1534)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 3303 759532 603530 397541 546268 047091 682720 973866 740983 359703 940984 > 2²¹¹ [i]