MinT - Best Known (90, 90+31, s)-Nets in Base 2

Best Known (90, 90+31, s)-Nets in Base 2

(90, 90+31, 135)-Net over F₂ — Constructive and digital

Digital (90, 121, 135)-net over F₂, using

2¹ times duplication [i] based on digital (89, 120, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 40, 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]

(90, 90+31, 176)-Net over F₂ — Digital

Digital (90, 121, 176)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(90, 90+31, 1622)-Net in Base 2 — Upper bound on s

There is no (90, 121, 1623)-net in base 2, because

1 times m-reduction [i] would yield (90, 120, 1623)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 334949 351390 310883 955582 767344 832876 > 2¹²⁰ [i]