MinT - Best Known (159−44, 159, s)-Nets in Base 2

Best Known (159−44, 159, s)-Nets in Base 2

(159−44, 159, 135)-Net over F₂ — Constructive and digital

Digital (115, 159, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 53, 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]

(159−44, 159, 179)-Net over F₂ — Digital

Digital (115, 159, 179)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(159−44, 159, 1324)-Net in Base 2 — Upper bound on s

There is no (115, 159, 1325)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 736281 166668 405020 489116 305005 325486 213711 693936 > 2¹⁵⁹ [i]