MinT - Best Known (84, 84+33, s)-Nets in Base 2

Best Known (84, 84+33, s)-Nets in Base 2

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

Digital (84, 117, 84)-net over F₂, using

t-expansion [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]

(84, 84+33, 135)-Net over F₂ — Digital

Digital (84, 117, 135)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+33, 1011)-Net in Base 2 — Upper bound on s

There is no (84, 117, 1012)-net in base 2, because

1 times m-reduction [i] would yield (84, 116, 1012)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 83210 462739 629806 156008 073800 188859 > 2¹¹⁶ [i]