MinT - Best Known (80, 80+29, s)-Nets in Base 3

Best Known (80, 80+29, s)-Nets in Base 3

(80, 80+29, 246)-Net over F₃ — Constructive and digital

Digital (80, 109, 246)-net over F₃, using

3¹ times duplication [i] based on digital (79, 108, 246)-net over F₃, using
- trace code for nets [i] based on digital (7, 36, 82)-net over F₂₇, using
  - net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
      - a function field by SÃ©mirat [i]

(80, 80+29, 420)-Net over F₃ — Digital

Digital (80, 109, 420)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+29, 14476)-Net in Base 3 — Upper bound on s

There is no (80, 109, 14477)-net in base 3, because

1 times m-reduction [i] would yield (80, 108, 14477)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3382 023132 997483 079563 707099 299546 342254 367606 584113 > 3¹⁰⁸ [i]