MinT - Best Known (133−41, 133, s)-Nets in Base 2

Best Known (133−41, 133, s)-Nets in Base 2

(133−41, 133, 72)-Net over F₂ — Constructive and digital

Digital (92, 133, 72)-net over F₂, using

2¹ times duplication [i] based on digital (91, 132, 72)-net over F₂, using
- trace code for nets [i] based on digital (3, 44, 24)-net over F₈, using
  - net from sequence [i] based on digital (3, 23)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]

(133−41, 133, 120)-Net over F₂ — Digital

Digital (92, 133, 120)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−41, 133, 776)-Net in Base 2 — Upper bound on s

There is no (92, 133, 777)-net in base 2, because

1 times m-reduction [i] would yield (92, 132, 777)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5505 175406 583598 596442 427116 809027 721696 > 2¹³² [i]