MinT - Best Known (99−33, 99, s)-Nets in Base 2

Best Known (99−33, 99, s)-Nets in Base 2

(99−33, 99, 66)-Net over F₂ — Constructive and digital

Digital (66, 99, 66)-net over F₂, using

3 times m-reduction [i] based on digital (66, 102, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 51, 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]

(99−33, 99, 80)-Net over F₂ — Digital

Digital (66, 99, 80)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−33, 99, 451)-Net in Base 2 — Upper bound on s

There is no (66, 99, 452)-net in base 2, because

1 times m-reduction [i] would yield (66, 98, 452)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 320835 158642 494239 403763 812644 > 2⁹⁸ [i]