MinT - Best Known (149−45, 149, s)-Nets in Base 3

Best Known (149−45, 149, s)-Nets in Base 3

(149−45, 149, 192)-Net over F₃ — Constructive and digital

Digital (104, 149, 192)-net over F₃, using

1 times m-reduction [i] based on digital (104, 150, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 50, 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]

(149−45, 149, 338)-Net over F₃ — Digital

Digital (104, 149, 338)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−45, 149, 7316)-Net in Base 3 — Upper bound on s

There is no (104, 149, 7317)-net in base 3, because

1 times m-reduction [i] would yield (104, 148, 7317)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41230 597489 439587 467983 331318 127009 612679 307715 916418 218972 946535 517473 > 3¹⁴⁸ [i]