MinT - Best Known (79, 79+27, s)-Nets in Base 3

Best Known (79, 79+27, s)-Nets in Base 3

(79, 79+27, 252)-Net over F₃ — Constructive and digital

Digital (79, 106, 252)-net over F₃, using

3¹ times duplication [i] based on digital (78, 105, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 35, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(79, 79+27, 478)-Net over F₃ — Digital

Digital (79, 106, 478)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(79, 79+27, 20219)-Net in Base 3 — Upper bound on s

There is no (79, 106, 20220)-net in base 3, because

1 times m-reduction [i] would yield (79, 105, 20220)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 125 242826 993983 123796 488332 794524 496303 987885 805017 > 3¹⁰⁵ [i]