MinT - Best Known (85−27, 85, s)-Nets in Base 2

Best Known (85−27, 85, s)-Nets in Base 2

(85−27, 85, 66)-Net over F₂ — Constructive and digital

Digital (58, 85, 66)-net over F₂, using

1 times m-reduction [i] based on digital (58, 86, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 43, 33)-net over F₄, using
  - net from sequence [i] based on digital (15, 32)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
      - an explicitly constructive algebraic function field [i]

(85−27, 85, 80)-Net over F₂ — Digital

Digital (58, 85, 80)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(85−27, 85, 480)-Net in Base 2 — Upper bound on s

There is no (58, 85, 481)-net in base 2, because

1 times m-reduction [i] would yield (58, 84, 481)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 19 441070 695701 556194 447504 > 2⁸⁴ [i]