MinT - Best Known (169−39, 169, s)-Nets in Base 3

Best Known (169−39, 169, s)-Nets in Base 3

(169−39, 169, 464)-Net over F₃ — Constructive and digital

Digital (130, 169, 464)-net over F₃, using

3¹ times duplication [i] based on digital (129, 168, 464)-net over F₃, using
- t-expansion [i] based on digital (128, 168, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 42, 116)-net over F₈₁, using
    - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]

(169−39, 169, 1013)-Net over F₃ — Digital

Digital (130, 169, 1013)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−39, 169, 65587)-Net in Base 3 — Upper bound on s

There is no (130, 169, 65588)-net in base 3, because

1 times m-reduction [i] would yield (130, 168, 65588)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 143 372395 560174 059538 712257 838144 132223 467030 253166 451373 053162 564713 143866 737009 > 3¹⁶⁸ [i]