MinT - Best Known (204−49, 204, s)-Nets in Base 3

Best Known (204−49, 204, s)-Nets in Base 3

(204−49, 204, 464)-Net over F₃ — Constructive and digital

Digital (155, 204, 464)-net over F₃, using

trace code for nets [i] based on digital (2, 51, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(204−49, 204, 1015)-Net over F₃ — Digital

Digital (155, 204, 1015)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(204−49, 204, 53185)-Net in Base 3 — Upper bound on s

There is no (155, 204, 53186)-net in base 3, because

1 times m-reduction [i] would yield (155, 203, 53186)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 173872 383359 117299 959237 610464 294448 525864 392633 980995 287026 366699 067799 636259 822924 173885 670129 > 3²⁰³ [i]