MinT - Best Known (93−27, 93, s)-Nets in Base 2

Best Known (93−27, 93, s)-Nets in Base 2

(93−27, 93, 75)-Net over F₂ — Constructive and digital

Digital (66, 93, 75)-net over F₂, using

trace code for nets [i] based on digital (4, 31, 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]

(93−27, 93, 106)-Net over F₂ — Digital

Digital (66, 93, 106)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(93−27, 93, 746)-Net in Base 2 — Upper bound on s

There is no (66, 93, 747)-net in base 2, because

1 times m-reduction [i] would yield (66, 92, 747)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5002 023603 576281 620170 050160 > 2⁹² [i]