MinT - Best Known (84, 84+31, s)-Nets in Base 2

Best Known (84, 84+31, s)-Nets in Base 2

(84, 84+31, 102)-Net over F₂ — Constructive and digital

Digital (84, 115, 102)-net over F₂, using

2¹ times duplication [i] based on digital (83, 114, 102)-net over F₂, using
- trace code for nets [i] based on digital (7, 38, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(84, 84+31, 150)-Net over F₂ — Digital

Digital (84, 115, 150)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+31, 1224)-Net in Base 2 — Upper bound on s

There is no (84, 115, 1225)-net in base 2, because

1 times m-reduction [i] would yield (84, 114, 1225)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 20921 227845 296629 003524 376270 352256 > 2¹¹⁴ [i]