MinT - Best Known (92, 147, s)-Nets in Base 2

Best Known (92, 147, s)-Nets in Base 2

(92, 147, 66)-Net over F₂ — Constructive and digital

Digital (92, 147, 66)-net over F₂, using

7 times m-reduction [i] based on digital (92, 154, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 77, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(92, 147, 83)-Net over F₂ — Digital

Digital (92, 147, 83)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(92, 147, 425)-Net in Base 2 — Upper bound on s

There is no (92, 147, 426)-net in base 2, because

1 times m-reduction [i] would yield (92, 146, 426)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 93 667868 803414 666751 538979 634202 024201 932696 > 2¹⁴⁶ [i]