MinT - Best Known (175−79, 175, s)-Nets in Base 3

Best Known (175−79, 175, s)-Nets in Base 3

(175−79, 175, 80)-Net over F₃ — Constructive and digital

Digital (96, 175, 80)-net over F₃, using

1 times m-reduction [i] based on digital (96, 176, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 88, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(175−79, 175, 119)-Net over F₃ — Digital

Digital (96, 175, 119)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−79, 175, 997)-Net in Base 3 — Upper bound on s

There is no (96, 175, 998)-net in base 3, because

1 times m-reduction [i] would yield (96, 174, 998)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 106713 828901 042349 837011 308755 936233 407109 848016 041683 946769 678155 216325 834194 231129 > 3¹⁷⁴ [i]