MinT - Best Known (204−63, 204, s)-Nets in Base 3

Best Known (204−63, 204, s)-Nets in Base 3

(204−63, 204, 204)-Net over F₃ — Constructive and digital

Digital (141, 204, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 68, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(204−63, 204, 411)-Net over F₃ — Digital

Digital (141, 204, 411)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−63, 204, 8237)-Net in Base 3 — Upper bound on s

There is no (141, 204, 8238)-net in base 3, because

1 times m-reduction [i] would yield (141, 203, 8238)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 195489 700513 077079 928526 926338 140475 957498 419557 429752 243235 309230 608157 278794 490376 483384 160009 > 3²⁰³ [i]