MinT - Best Known (104−31, 104, s)-Nets in Base 2

Best Known (104−31, 104, s)-Nets in Base 2

(104−31, 104, 72)-Net over F₂ — Constructive and digital

Digital (73, 104, 72)-net over F₂, using

1 times m-reduction [i] based on digital (73, 105, 72)-net over F₂, using
- trace code for nets [i] based on digital (3, 35, 24)-net over F₈, using
  - net from sequence [i] based on digital (3, 23)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]

(104−31, 104, 108)-Net over F₂ — Digital

Digital (73, 104, 108)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(104−31, 104, 727)-Net in Base 2 — Upper bound on s

There is no (73, 104, 728)-net in base 2, because

1 times m-reduction [i] would yield (73, 103, 728)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 10 160587 332831 021244 929749 886718 > 2¹⁰³ [i]