MinT - Best Known (100−31, 100, s)-Nets in Base 2

Best Known (100−31, 100, s)-Nets in Base 2

(100−31, 100, 66)-Net over F₂ — Constructive and digital

Digital (69, 100, 66)-net over F₂, using

8 times m-reduction [i] based on digital (69, 108, 66)-net over F₂, using
- trace code for nets [i] based on digital (15, 54, 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]

(100−31, 100, 95)-Net over F₂ — Digital

Digital (69, 100, 95)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(100−31, 100, 601)-Net in Base 2 — Upper bound on s

There is no (69, 100, 602)-net in base 2, because

1 times m-reduction [i] would yield (69, 99, 602)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 642196 047987 933589 183492 255448 > 2⁹⁹ [i]