MinT - Best Known (165, 165+69, s)-Nets in Base 2

Best Known (165, 165+69, s)-Nets in Base 2

(165, 165+69, 135)-Net over F₂ — Constructive and digital

Digital (165, 234, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 78, 45)-net over F₈, using
- net from sequence [i] based on digital (9, 44)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
    - an explicitly constructive algebraic function field [i]

(165, 165+69, 212)-Net over F₂ — Digital

Digital (165, 234, 212)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(165, 165+69, 1514)-Net in Base 2 — Upper bound on s

There is no (165, 234, 1515)-net in base 2, because

1 times m-reduction [i] would yield (165, 233, 1515)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13839 450572 436596 134312 807638 318552 919259 625634 508649 938556 125016 003103 > 2²³³ [i]