MinT - Best Known (100, 100+33, s)-Nets in Base 2

Best Known (100, 100+33, s)-Nets in Base 2

(100, 100+33, 144)-Net over F₂ — Constructive and digital

Digital (100, 133, 144)-net over F₂, using

2¹ times duplication [i] based on digital (99, 132, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 44, 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]

(100, 100+33, 205)-Net over F₂ — Digital

Digital (100, 133, 205)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 100+33, 2046)-Net in Base 2 — Upper bound on s

There is no (100, 133, 2047)-net in base 2, because

1 times m-reduction [i] would yield (100, 132, 2047)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5447 289983 925892 821352 178449 499843 817073 > 2¹³² [i]