MinT - Best Known (174−49, 174, s)-Nets in Base 2

Best Known (174−49, 174, s)-Nets in Base 2

(174−49, 174, 135)-Net over F₂ — Constructive and digital

Digital (125, 174, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 58, 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]

(174−49, 174, 185)-Net over F₂ — Digital

Digital (125, 174, 185)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−49, 174, 1414)-Net in Base 2 — Upper bound on s

There is no (125, 174, 1415)-net in base 2, because

1 times m-reduction [i] would yield (125, 173, 1415)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 12047 750666 516781 692541 278948 390598 980263 730053 905104 > 2¹⁷³ [i]