MinT - Best Known (155−47, 155, s)-Nets in Base 3

Best Known (155−47, 155, s)-Nets in Base 3

(155−47, 155, 192)-Net over F₃ — Constructive and digital

Digital (108, 155, 192)-net over F₃, using

1 times m-reduction [i] based on digital (108, 156, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 52, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(155−47, 155, 345)-Net over F₃ — Digital

Digital (108, 155, 345)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(155−47, 155, 7357)-Net in Base 3 — Upper bound on s

There is no (108, 155, 7358)-net in base 3, because

1 times m-reduction [i] would yield (108, 154, 7358)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30 000587 036516 206350 686823 028720 538667 168111 578207 050058 065871 462937 022617 > 3¹⁵⁴ [i]