MinT - Best Known (165−67, 165, s)-Nets in Base 2

Best Known (165−67, 165, s)-Nets in Base 2

(165−67, 165, 66)-Net over F₂ — Constructive and digital

Digital (98, 165, 66)-net over F₂, using

1 times m-reduction [i] based on digital (98, 166, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 83, 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]

(165−67, 165, 76)-Net over F₂ — Digital

Digital (98, 165, 76)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(165−67, 165, 365)-Net in Base 2 — Upper bound on s

There is no (98, 165, 366)-net in base 2, because

1 times m-reduction [i] would yield (98, 164, 366)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 23 462938 354936 098243 563480 473774 864203 091790 176605 > 2¹⁶⁴ [i]