MinT - Best Known (209−61, 209, s)-Nets in Base 3

Best Known (209−61, 209, s)-Nets in Base 3

(209−61, 209, 252)-Net over F₃ — Constructive and digital

Digital (148, 209, 252)-net over F₃, using

1 times m-reduction [i] based on digital (148, 210, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 70, 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]

(209−61, 209, 503)-Net over F₃ — Digital

Digital (148, 209, 503)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−61, 209, 12211)-Net in Base 3 — Upper bound on s

There is no (148, 209, 12212)-net in base 3, because

1 times m-reduction [i] would yield (148, 208, 12212)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1746 816652 267122 197595 711217 626177 983273 762631 723274 017600 110396 311411 977850 288464 338486 609482 158073 > 3²⁰⁸ [i]