MinT - Best Known (88, 88+67, s)-Nets in Base 2

Best Known (88, 88+67, s)-Nets in Base 2

(88, 88+67, 54)-Net over F₂ — Constructive and digital

Digital (88, 155, 54)-net over F₂, using

1 times m-reduction [i] based on digital (88, 156, 54)-net over F₂, using
- trace code for nets [i] based on digital (10, 78, 27)-net over F₄, using
  - net from sequence [i] based on digital (10, 26)-sequence over F₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
      - an explicitly constructive algebraic function field [i]

(88, 88+67, 63)-Net over F₂ — Digital

Digital (88, 155, 63)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+67, 288)-Net in Base 2 — Upper bound on s

There is no (88, 155, 289)-net in base 2, because

1 times m-reduction [i] would yield (88, 154, 289)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 24343 621972 702127 876410 861119 396166 896887 323506 > 2¹⁵⁴ [i]