MinT - Best Known (75, 75+63, s)-Nets in Base 3

Best Known (75, 75+63, s)-Nets in Base 3

(75, 75+63, 68)-Net over F₃ — Constructive and digital

Digital (75, 138, 68)-net over F₃, using

trace code for nets [i] based on digital (6, 69, 34)-net over F₉, using
- net from sequence [i] based on digital (6, 33)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
    - a function field by SÃ©mirat [i]

(75, 75+63, 94)-Net over F₃ — Digital

Digital (75, 138, 94)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+63, 767)-Net in Base 3 — Upper bound on s

There is no (75, 138, 768)-net in base 3, because

1 times m-reduction [i] would yield (75, 137, 768)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 239544 901130 627133 430833 125345 405405 672438 540389 986325 523825 927169 > 3¹³⁷ [i]