MinT - Best Known (102, 102+33, s)-Nets in Base 2

Best Known (102, 102+33, s)-Nets in Base 2

(102, 102+33, 144)-Net over F₂ — Constructive and digital

Digital (102, 135, 144)-net over F₂, using

t-expansion [i] based on digital (101, 135, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 45, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]

(102, 102+33, 215)-Net over F₂ — Digital

Digital (102, 135, 215)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 102+33, 2234)-Net in Base 2 — Upper bound on s

There is no (102, 135, 2235)-net in base 2, because

1 times m-reduction [i] would yield (102, 134, 2235)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 21885 803074 087523 151029 644855 668460 158985 > 2¹³⁴ [i]