MinT - Best Known (204−89, 204, s)-Nets in Base 3

Best Known (204−89, 204, s)-Nets in Base 3

(204−89, 204, 128)-Net over F₃ — Constructive and digital

Digital (115, 204, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 102, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(204−89, 204, 149)-Net over F₃ — Digital

Digital (115, 204, 149)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−89, 204, 1328)-Net in Base 3 — Upper bound on s

There is no (115, 204, 1329)-net in base 3, because

1 times m-reduction [i] would yield (115, 203, 1329)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 301069 624371 080875 763240 354559 625376 513613 581579 793248 000161 950830 898873 102971 077490 100990 915569 > 3²⁰³ [i]