MinT - Best Known (90, 90+60, s)-Nets in Base 2

Best Known (90, 90+60, s)-Nets in Base 2

(90, 90+60, 66)-Net over F₂ — Constructive and digital

Digital (90, 150, 66)-net over F₂, using

trace code for nets [i] based on digital (15, 75, 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]

(90, 90+60, 73)-Net over F₂ — Digital

Digital (90, 150, 73)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+60, 343)-Net in Base 2 — Upper bound on s

There is no (90, 150, 344)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1527 552421 427356 453133 651576 106148 588095 853480 > 2¹⁵⁰ [i]