MinT - Best Known (74, 74+23, s)-Nets in Base 2

Best Known (74, 74+23, s)-Nets in Base 2

(74, 74+23, 135)-Net over F₂ — Constructive and digital

Digital (74, 97, 135)-net over F₂, using

2¹ times duplication [i] based on digital (73, 96, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 32, 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]

(74, 74+23, 183)-Net over F₂ — Digital

Digital (74, 97, 183)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+23, 2064)-Net in Base 2 — Upper bound on s

There is no (74, 97, 2065)-net in base 2, because

1 times m-reduction [i] would yield (74, 96, 2065)-net in base 2, but
- the generalized Rao bound for nets shows that 2^mÂ â‰¥ 79379 949603 676425 783783 731568 > 2⁹⁶ [i]