MinT - Best Known (159, 159+65, s)-Nets in Base 2

Best Known (159, 159+65, s)-Nets in Base 2

(159, 159+65, 135)-Net over F₂ — Constructive and digital

Digital (159, 224, 135)-net over F₂, using

1 times m-reduction [i] based on digital (159, 225, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 75, 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]

(159, 159+65, 213)-Net over F₂ — Digital

Digital (159, 224, 213)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(159, 159+65, 1555)-Net in Base 2 — Upper bound on s

There is no (159, 224, 1556)-net in base 2, because

1 times m-reduction [i] would yield (159, 223, 1556)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 13 694214 714911 018934 296482 314436 015409 185652 632004 581396 904988 303088 > 2²²³ [i]