MinT - Best Known (82−20, 82, s)-Nets in Base 2

Best Known (82−20, 82, s)-Nets in Base 2

(82−20, 82, 102)-Net over F₂ — Constructive and digital

Digital (62, 82, 102)-net over F₂, using

2¹ times duplication [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]

(82−20, 82, 151)-Net over F₂ — Digital

Digital (62, 82, 151)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(82−20, 82, 1317)-Net in Base 2 — Upper bound on s

There is no (62, 82, 1318)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4 860491 738935 604348 057144 > 2⁸² [i]