MinT - Best Known (194−81, 194, s)-Nets in Base 3

Best Known (194−81, 194, s)-Nets in Base 3

(194−81, 194, 128)-Net over F₃ — Constructive and digital

Digital (113, 194, 128)-net over F₃, using

6 times m-reduction [i] based on digital (113, 200, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 100, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(194−81, 194, 161)-Net over F₃ — Digital

Digital (113, 194, 161)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−81, 194, 1541)-Net in Base 3 — Upper bound on s

There is no (113, 194, 1542)-net in base 3, because

1 times m-reduction [i] would yield (113, 193, 1542)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 122 421739 532259 211914 233939 947268 816387 517175 417379 002501 054502 959726 198344 201614 977871 004945 > 3¹⁹³ [i]