MinT - Best Known (71, 71+27, s)-Nets in Base 3

Best Known (71, 71+27, s)-Nets in Base 3

(71, 71+27, 204)-Net over F₃ — Constructive and digital

Digital (71, 98, 204)-net over F₃, using

1 times m-reduction [i] based on digital (71, 99, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 33, 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]

(71, 71+27, 341)-Net over F₃ — Digital

Digital (71, 98, 341)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+27, 10277)-Net in Base 3 — Upper bound on s

There is no (71, 98, 10278)-net in base 3, because

1 times m-reduction [i] would yield (71, 97, 10278)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 19088 875182 064485 248555 037335 494173 933858 088469 > 3⁹⁷ [i]