MinT - Best Known (80−19, 80, s)-Nets in Base 2

Best Known (80−19, 80, s)-Nets in Base 2

(80−19, 80, 102)-Net over F₂ — Constructive and digital

Digital (61, 80, 102)-net over F₂, using

1 times m-reduction [i] based on digital (61, 81, 102)-net over F₂, using
- trace code for nets [i] based on digital (7, 27, 34)-net over F₈, using
  - net from sequence [i] based on digital (7, 33)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
      - a function field by SÃ©mirat [i]

(80−19, 80, 161)-Net over F₂ — Digital

Digital (61, 80, 161)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(80−19, 80, 1807)-Net in Base 2 — Upper bound on s

There is no (61, 80, 1808)-net in base 2, because

1 times m-reduction [i] would yield (61, 79, 1808)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 606649 724155 953133 258387 > 2⁷⁹ [i]