MinT - Best Known (142−30, 142, s)-Nets in Base 2

Best Known (142−30, 142, s)-Nets in Base 2

(142−30, 142, 196)-Net over F₂ — Constructive and digital

Digital (112, 142, 196)-net over F₂, using

2² times duplication [i] based on digital (110, 140, 196)-net over F₂, using
- trace code for nets [i] based on digital (5, 35, 49)-net over F₁₆, using
  - net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
      - a function field by SÃ©mirat [i]

(142−30, 142, 337)-Net over F₂ — Digital

Digital (112, 142, 337)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−30, 142, 4522)-Net in Base 2 — Upper bound on s

There is no (112, 142, 4523)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 577501 818785 702623 508057 788342 556946 262096 > 2¹⁴² [i]