MinT - Best Known (247−70, 247, s)-Nets in Base 3

Best Known (247−70, 247, s)-Nets in Base 3

(247−70, 247, 288)-Net over F₃ — Constructive and digital

Digital (177, 247, 288)-net over F₃, using

2 times m-reduction [i] based on digital (177, 249, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 83, 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]

(247−70, 247, 642)-Net over F₃ — Digital

Digital (177, 247, 642)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(247−70, 247, 16159)-Net in Base 3 — Upper bound on s

There is no (177, 247, 16160)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7073 794674 785216 359981 691660 676625 000936 011030 876769 749610 819430 754718 047483 058970 257147 172754 634805 321276 107460 407425 > 3²⁴⁷ [i]