MinT - Best Known (234−65, 234, s)-Nets in Base 3

Best Known (234−65, 234, s)-Nets in Base 3

(234−65, 234, 288)-Net over F₃ — Constructive and digital

Digital (169, 234, 288)-net over F₃, using

3 times m-reduction [i] based on digital (169, 237, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 79, 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]

(234−65, 234, 656)-Net over F₃ — Digital

Digital (169, 234, 656)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(234−65, 234, 19018)-Net in Base 3 — Upper bound on s

There is no (169, 234, 19019)-net in base 3, because

1 times m-reduction [i] would yield (169, 233, 19019)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1478 346948 209140 923284 693652 527028 618937 163961 605158 880982 579578 563569 416662 533993 560554 366876 744484 591026 394049 > 3²³³ [i]