MinT - Best Known (80−20, 80, s)-Nets in Base 2

Best Known (80−20, 80, s)-Nets in Base 2

(80−20, 80, 84)-Net over F₂ — Constructive and digital

Digital (60, 80, 84)-net over F₂, using

t-expansion [i] based on digital (59, 80, 84)-net over F₂, using
- 1 times m-reduction [i] based on digital (59, 81, 84)-net over F₂, using
  - trace code for nets [i] based on digital (5, 27, 28)-net over F₈, using
    - net from sequence [i] based on digital (5, 27)-sequence over F₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
        a function field by SÃ©mirat [i]

(80−20, 80, 139)-Net over F₂ — Digital

Digital (60, 80, 139)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(80−20, 80, 1144)-Net in Base 2 — Upper bound on s

There is no (60, 80, 1145)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 209601 727163 671184 793044 > 2⁸⁰ [i]