MinT - Best Known (193−77, 193, s)-Nets in Base 3

Best Known (193−77, 193, s)-Nets in Base 3

(193−77, 193, 148)-Net over F₃ — Constructive and digital

Digital (116, 193, 148)-net over F₃, using

5 times m-reduction [i] based on digital (116, 198, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 99, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(193−77, 193, 182)-Net over F₃ — Digital

Digital (116, 193, 182)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−77, 193, 1896)-Net in Base 3 — Upper bound on s

There is no (116, 193, 1897)-net in base 3, because

1 times m-reduction [i] would yield (116, 192, 1897)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 519931 310430 977538 360100 633536 098822 983974 505803 191454 444712 704760 370525 352187 014249 571433 > 3¹⁹² [i]