MinT - Best Known (90, 90+30, s)-Nets in Base 2

Best Known (90, 90+30, s)-Nets in Base 2

(90, 90+30, 138)-Net over F₂ — Constructive and digital

Digital (90, 120, 138)-net over F₂, using

trace code for nets [i] based on digital (10, 40, 46)-net over F₈, using
- net from sequence [i] based on digital (10, 45)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ III based on the algebraic function field F/F₈ with g(F)Â =Â 9, N(F)Â =Â 45, and 1 place with degree 2 [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]

(90, 90+30, 186)-Net over F₂ — Digital

Digital (90, 120, 186)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+30, 1622)-Net in Base 2 — Upper bound on s

There is no (90, 120, 1623)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 334949 351390 310883 955582 767344 832876 > 2¹²⁰ [i]