MinT - Best Known (105−35, 105, s)-Nets in Base 2

Best Known (105−35, 105, s)-Nets in Base 2

(105−35, 105, 66)-Net over F₂ — Constructive and digital

Digital (70, 105, 66)-net over F₂, using

5 times m-reduction [i] based on digital (70, 110, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 55, 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]

(105−35, 105, 84)-Net over F₂ — Digital

Digital (70, 105, 84)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−35, 105, 473)-Net in Base 2 — Upper bound on s

There is no (70, 105, 474)-net in base 2, because

1 times m-reduction [i] would yield (70, 104, 474)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 20 344082 073734 128297 521959 686329 > 2¹⁰⁴ [i]