MinT - Best Known (210−90, 210, s)-Nets in Base 2

Best Known (210−90, 210, s)-Nets in Base 2

(210−90, 210, 66)-Net over F₂ — Constructive and digital

Digital (120, 210, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 105, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(210−90, 210, 82)-Net over F₂ — Digital

Digital (120, 210, 82)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(210−90, 210, 384)-Net in Base 2 — Upper bound on s

There is no (120, 210, 385)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1656 458867 368235 008552 673433 922458 276171 772574 291690 202868 323136 > 2²¹⁰ [i]