MinT - Best Known (129−31, 129, s)-Nets in Base 2

Best Known (129−31, 129, s)-Nets in Base 2

(129−31, 129, 144)-Net over F₂ — Constructive and digital

Digital (98, 129, 144)-net over F₂, using

t-expansion [i] based on digital (97, 129, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 43, 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]

(129−31, 129, 217)-Net over F₂ — Digital

Digital (98, 129, 217)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−31, 129, 2357)-Net in Base 2 — Upper bound on s

There is no (98, 129, 2358)-net in base 2, because

1 times m-reduction [i] would yield (98, 128, 2358)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 340 332787 648356 279621 907921 586366 431520 > 2¹²⁸ [i]