MinT - Best Known (119, 119+46, s)-Nets in Base 2

Best Known (119, 119+46, s)-Nets in Base 2

(119, 119+46, 135)-Net over F₂ — Constructive and digital

Digital (119, 165, 135)-net over F₂, using

trace code for nets [i] based on digital (9, 55, 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]

(119, 119+46, 181)-Net over F₂ — Digital

Digital (119, 165, 181)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+46, 1327)-Net in Base 2 — Upper bound on s

There is no (119, 165, 1328)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 46 857140 662856 147008 513689 081676 681543 323245 633538 > 2¹⁶⁵ [i]