MinT - Best Known (75−22, 75, s)-Nets in Base 3

Best Known (75−22, 75, s)-Nets in Base 3

(75−22, 75, 156)-Net over F₃ — Constructive and digital

Digital (53, 75, 156)-net over F₃, using

trace code for nets [i] based on digital (3, 25, 52)-net over F₂₇, using
- net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
    - a function field by SÃ©mirat [i]

(75−22, 75, 226)-Net over F₃ — Digital

Digital (53, 75, 226)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−22, 75, 4385)-Net in Base 3 — Upper bound on s

There is no (53, 75, 4386)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 608612 222417 798767 067856 679982 894081 > 3⁷⁵ [i]