MinT - Best Known (199−55, 199, s)-Nets in Base 3

Best Known (199−55, 199, s)-Nets in Base 3

(199−55, 199, 288)-Net over F₃ — Constructive and digital

Digital (144, 199, 288)-net over F₃, using

3¹ times duplication [i] based on digital (143, 198, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 66, 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]

(199−55, 199, 581)-Net over F₃ — Digital

Digital (144, 199, 581)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−55, 199, 17202)-Net in Base 3 — Upper bound on s

There is no (144, 199, 17203)-net in base 3, because

1 times m-reduction [i] would yield (144, 198, 17203)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29524 171153 449849 557373 709803 770926 106245 350371 746062 464252 542524 604346 899516 546169 083829 937083 > 3¹⁹⁸ [i]