MinT - Best Known (106−31, 106, s)-Nets in Base 2

Best Known (106−31, 106, s)-Nets in Base 2

(106−31, 106, 75)-Net over F₂ — Constructive and digital

Digital (75, 106, 75)-net over F₂, using

2¹ times duplication [i] based on digital (74, 105, 75)-net over F₂, using
- trace code for nets [i] based on digital (4, 35, 25)-net over F₈, using
  - net from sequence [i] based on digital (4, 24)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
      - a function field by SÃ©mirat [i]

(106−31, 106, 114)-Net over F₂ — Digital

Digital (75, 106, 114)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−31, 106, 800)-Net in Base 2 — Upper bound on s

There is no (75, 106, 801)-net in base 2, because

1 times m-reduction [i] would yield (75, 105, 801)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 40 965527 995945 018828 974138 467328 > 2¹⁰⁵ [i]