MinT - Best Known (68, 95, s)-Nets in Base 3

Best Known (68, 95, s)-Nets in Base 3

(68, 95, 192)-Net over F₃ — Constructive and digital

Digital (68, 95, 192)-net over F₃, using

1 times m-reduction [i] based on digital (68, 96, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 32, 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]

(68, 95, 297)-Net over F₃ — Digital

Digital (68, 95, 297)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 95, 7973)-Net in Base 3 — Upper bound on s

There is no (68, 95, 7974)-net in base 3, because

1 times m-reduction [i] would yield (68, 94, 7974)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 707 519285 358870 491922 175379 920309 615496 776725 > 3⁹⁴ [i]