MinT - Best Known (175−69, 175, s)-Nets in Base 2

Best Known (175−69, 175, s)-Nets in Base 2

(175−69, 175, 66)-Net over F₂ — Constructive and digital

Digital (106, 175, 66)-net over F₂, using

7 times m-reduction [i] based on digital (106, 182, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 91, 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]

(175−69, 175, 85)-Net over F₂ — Digital

Digital (106, 175, 85)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−69, 175, 421)-Net in Base 2 — Upper bound on s

There is no (106, 175, 422)-net in base 2, because

1 times m-reduction [i] would yield (106, 174, 422)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 24328 982970 089978 007172 171182 018989 734613 676283 043514 > 2¹⁷⁴ [i]