MinT - Best Known (64, 114, s)-Nets in Base 9

Best Known (64, 114, s)-Nets in Base 9

(64, 114, 344)-Net over F₉ — Constructive and digital

Digital (64, 114, 344)-net over F₉, using

trace code for nets [i] based on digital (7, 57, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(64, 114, 390)-Net over F₉ — Digital

Digital (64, 114, 390)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 114, 28552)-Net in Base 9 — Upper bound on s

There is no (64, 114, 28553)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 076402 380486 750344 388257 666243 775894 718440 116402 565751 927949 438545 148596 698007 402085 219977 671902 549243 152905 > 9¹¹⁴ [i]