MinT - Best Known (76, 76+24, s)-Nets in Base 2

Best Known (76, 76+24, s)-Nets in Base 2

(76, 76+24, 135)-Net over F₂ — Constructive and digital

Digital (76, 100, 135)-net over F₂, using

2¹ times duplication [i] based on digital (75, 99, 135)-net over F₂, using
- trace code for nets [i] based on digital (9, 33, 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]

(76, 76+24, 181)-Net over F₂ — Digital

Digital (76, 100, 181)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+24, 1688)-Net in Base 2 — Upper bound on s

There is no (76, 100, 1689)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 1 272603 206575 617602 987783 182092 > 2¹⁰⁰ [i]