MinT - Best Known (231−69, 231, s)-Nets in Base 3

Best Known (231−69, 231, s)-Nets in Base 3

(231−69, 231, 252)-Net over F₃ — Constructive and digital

Digital (162, 231, 252)-net over F₃, using

trace code for nets [i] based on digital (8, 77, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(231−69, 231, 510)-Net over F₃ — Digital

Digital (162, 231, 510)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(231−69, 231, 11396)-Net in Base 3 — Upper bound on s

There is no (162, 231, 11397)-net in base 3, because

1 times m-reduction [i] would yield (162, 230, 11397)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 830233 944323 010948 533667 407269 531518 535199 197068 607121 884801 013079 569898 392967 221109 563594 919500 167397 139921 > 3²³⁰ [i]