MinT - Best Known (99, 99+31, s)-Nets in Base 2

Best Known (99, 99+31, s)-Nets in Base 2

(99, 99+31, 144)-Net over F₂ — Constructive and digital

Digital (99, 130, 144)-net over F₂, using

2 times m-reduction [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]

(99, 99+31, 223)-Net over F₂ — Digital

Digital (99, 130, 223)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+31, 2470)-Net in Base 2 — Upper bound on s

There is no (99, 130, 2471)-net in base 2, because

1 times m-reduction [i] would yield (99, 129, 2471)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 682 504932 864125 290303 269136 308086 225496 > 2¹²⁹ [i]