MinT - Best Known (68, 68+26, s)-Nets in Base 3

Best Known (68, 68+26, s)-Nets in Base 3

(68, 68+26, 204)-Net over F₃ — Constructive and digital

Digital (68, 94, 204)-net over F₃, using

3¹ times duplication [i] based on digital (67, 93, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 31, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(68, 68+26, 326)-Net over F₃ — Digital

Digital (68, 94, 326)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(68, 68+26, 7973)-Net in Base 3 — Upper bound on s

There is no (68, 94, 7974)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 707 519285 358870 491922 175379 920309 615496 776725 > 3⁹⁴ [i]