MinT - Best Known (83, 83+33, s)-Nets in Base 2

Best Known (83, 83+33, s)-Nets in Base 2

(83, 83+33, 84)-Net over F₂ — Constructive and digital

Digital (83, 116, 84)-net over F₂, using

1 times m-reduction [i] based on digital (83, 117, 84)-net over F₂, using
- trace code for nets [i] based on digital (5, 39, 28)-net over F₈, using
  - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
      - a function field by SÃ©mirat [i]

(83, 83+33, 131)-Net over F₂ — Digital

Digital (83, 116, 131)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(83, 83+33, 968)-Net in Base 2 — Upper bound on s

There is no (83, 116, 969)-net in base 2, because

1 times m-reduction [i] would yield (83, 115, 969)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 42201 066094 040633 937192 380713 530380 > 2¹¹⁵ [i]