MinT - Best Known (169, 169+78, s)-Nets in Base 3

Best Known (169, 169+78, s)-Nets in Base 3

(169, 169+78, 192)-Net over F₃ — Constructive and digital

Digital (169, 247, 192)-net over F₃, using

3¹ times duplication [i] based on digital (168, 246, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 82, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(169, 169+78, 453)-Net over F₃ — Digital

Digital (169, 247, 453)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(169, 169+78, 8055)-Net in Base 3 — Upper bound on s

There is no (169, 247, 8056)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7076 788562 203746 632210 845786 522998 018551 336722 851011 026449 710723 690566 215892 473959 853075 492078 408035 930672 089180 113057 > 3²⁴⁷ [i]