MinT - Best Known (83, 83+39, s)-Nets in Base 2

Best Known (83, 83+39, s)-Nets in Base 2

(83, 83+39, 68)-Net over F₂ — Constructive and digital

Digital (83, 122, 68)-net over F₂, using

2 times m-reduction [i] based on digital (83, 124, 68)-net over F₂, using
- trace code for nets [i] based on digital (21, 62, 34)-net over F₄, using
  - net from sequence [i] based on digital (21, 33)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 21 and N(F) ≥ 34, using
      - T₅ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(83, 83+39, 103)-Net over F₂ — Digital

Digital (83, 122, 103)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+39, 627)-Net in Base 2 — Upper bound on s

There is no (83, 122, 628)-net in base 2, because

1 times m-reduction [i] would yield (83, 121, 628)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 2 687745 808795 782907 047998 162629 290197 > 2¹²¹ [i]