MinT - Best Known (195−55, 195, s)-Nets in Base 3

Best Known (195−55, 195, s)-Nets in Base 3

(195−55, 195, 282)-Net over F₃ — Constructive and digital

Digital (140, 195, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 65, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(195−55, 195, 532)-Net over F₃ — Digital

Digital (140, 195, 532)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−55, 195, 14614)-Net in Base 3 — Upper bound on s

There is no (140, 195, 14615)-net in base 3, because

1 times m-reduction [i] would yield (140, 194, 14615)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 364 436182 765823 943570 301248 950985 473350 229449 038413 575554 518795 904228 895274 586594 080525 999531 > 3¹⁹⁴ [i]