MinT - Best Known (164, 164+65, s)-Nets in Base 3

Best Known (164, 164+65, s)-Nets in Base 3

(164, 164+65, 288)-Net over F₃ — Constructive and digital

Digital (164, 229, 288)-net over F₃, using

3¹ times duplication [i] based on digital (163, 228, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 76, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(164, 164+65, 598)-Net over F₃ — Digital

Digital (164, 229, 598)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(164, 164+65, 16013)-Net in Base 3 — Upper bound on s

There is no (164, 229, 16014)-net in base 3, because

1 times m-reduction [i] would yield (164, 228, 16014)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 082329 076979 039862 885252 704890 398431 831757 369786 758418 706090 515600 069090 062265 279889 444188 036683 240961 778497 > 3²²⁸ [i]