MinT - Best Known (215−60, 215, s)-Nets in Base 2

Best Known (215−60, 215, s)-Nets in Base 2

(215−60, 215, 144)-Net over F₂ — Constructive and digital

Digital (155, 215, 144)-net over F₂, using

1 times m-reduction [i] based on digital (155, 216, 144)-net over F₂, using
- trace code for nets [i] based on digital (11, 72, 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]

(215−60, 215, 225)-Net over F₂ — Digital

Digital (155, 215, 225)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−60, 215, 1686)-Net in Base 2 — Upper bound on s

There is no (155, 215, 1687)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 53104 231905 060484 426942 137922 121434 625132 363887 630858 583583 212976 > 2²¹⁵ [i]