MinT - Best Known (78, 78+29, s)-Nets in Base 3

Best Known (78, 78+29, s)-Nets in Base 3

(78, 78+29, 228)-Net over F₃ — Constructive and digital

Digital (78, 107, 228)-net over F₃, using

1 times m-reduction [i] based on digital (78, 108, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 36, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(78, 78+29, 386)-Net over F₃ — Digital

Digital (78, 107, 386)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+29, 12372)-Net in Base 3 — Upper bound on s

There is no (78, 107, 12373)-net in base 3, because

1 times m-reduction [i] would yield (78, 106, 12373)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 376 087639 491980 263351 301764 235494 408621 136071 630209 > 3¹⁰⁶ [i]