MinT - Best Known (72, 72+30, s)-Nets in Base 2

Best Known (72, 72+30, s)-Nets in Base 2

(72, 72+30, 75)-Net over F₂ — Constructive and digital

Digital (72, 102, 75)-net over F₂, using

trace code for nets [i] based on digital (4, 34, 25)-net over F₈, using
- net from sequence [i] based on digital (4, 24)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
    - a function field by SÃ©mirat [i]

(72, 72+30, 110)-Net over F₂ — Digital

Digital (72, 102, 110)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+30, 694)-Net in Base 2 — Upper bound on s

There is no (72, 102, 695)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 5 170750 617068 604535 855801 739668 > 2¹⁰² [i]