MinT - Best Known (72−20, 72, s)-Nets in Base 2

Best Known (72−20, 72, s)-Nets in Base 2

(72−20, 72, 75)-Net over F₂ — Constructive and digital

Digital (52, 72, 75)-net over F₂, using

trace code for nets [i] based on digital (4, 24, 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]

(72−20, 72, 98)-Net over F₂ — Digital

Digital (52, 72, 98)-net over F₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(72−20, 72, 651)-Net in Base 2 — Upper bound on s

There is no (52, 72, 652)-net in base 2, because

the generalized Rao bound for nets shows that 2^mÂ â‰¥ 4756 947691 435970 797099 > 2⁷² [i]