MinT - Best Known (231−71, 231, s)-Nets in Base 3

Best Known (231−71, 231, s)-Nets in Base 3

(231−71, 231, 228)-Net over F₃ — Constructive and digital

Digital (160, 231, 228)-net over F₃, using

trace code for nets [i] based on digital (6, 77, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]

(231−71, 231, 466)-Net over F₃ — Digital

Digital (160, 231, 466)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−71, 231, 9462)-Net in Base 3 — Upper bound on s

There is no (160, 231, 9463)-net in base 3, because

1 times m-reduction [i] would yield (160, 230, 9463)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 709047 991485 644871 036412 885012 060100 882145 382493 064806 719384 664632 434190 464639 392615 529993 363669 253570 843803 > 3²³⁰ [i]