MinT - Best Known (94, 94+42, s)-Nets in Base 2

Best Known (94, 94+42, s)-Nets in Base 2

(94, 94+42, 72)-Net over F₂ — Constructive and digital

Digital (94, 136, 72)-net over F₂, using

2¹ times duplication [i] based on digital (93, 135, 72)-net over F₂, using
- trace code for nets [i] based on digital (3, 45, 24)-net over F₈, using
  - net from sequence [i] based on digital (3, 23)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
      - the Klein quartic over F₈ [i]

(94, 94+42, 122)-Net over F₂ — Digital

Digital (94, 136, 122)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 94+42, 742)-Net in Base 2 — Upper bound on s

There is no (94, 136, 743)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 88856 125161 162278 039008 177811 509277 654328 > 2¹³⁶ [i]