MinT - Best Known (130, 130+49, s)-Nets in Base 3

Best Known (130, 130+49, s)-Nets in Base 3

(130, 130+49, 282)-Net over F₃ — Constructive and digital

Digital (130, 179, 282)-net over F₃, using

1 times m-reduction [i] based on digital (130, 180, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 60, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(130, 130+49, 551)-Net over F₃ — Digital

Digital (130, 179, 551)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(130, 130+49, 16919)-Net in Base 3 — Upper bound on s

There is no (130, 179, 16920)-net in base 3, because

1 times m-reduction [i] would yield (130, 178, 16920)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 473852 392179 637264 551206 403565 975981 423663 135434 692161 844608 022024 300417 035033 281793 > 3¹⁷⁸ [i]