MinT - Best Known (172, 172+68, s)-Nets in Base 3

Best Known (172, 172+68, s)-Nets in Base 3

(172, 172+68, 288)-Net over F₃ — Constructive and digital

Digital (172, 240, 288)-net over F₃, using

t-expansion [i] based on digital (171, 240, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 80, 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]

(172, 172+68, 627)-Net over F₃ — Digital

Digital (172, 240, 627)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(172, 172+68, 15755)-Net in Base 3 — Upper bound on s

There is no (172, 240, 15756)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 231114 510642 599442 302080 986756 777992 661193 402476 351142 563012 866995 566052 584190 292744 022609 368401 429450 496854 149225 > 3²⁴⁰ [i]