MinT - Best Known (75, 75+41, s)-Nets in Base 3

Best Known (75, 75+41, s)-Nets in Base 3

(75, 75+41, 148)-Net over F₃ — Constructive and digital

Digital (75, 116, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 58, 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]

(75, 75+41, 170)-Net over F₃ — Digital

Digital (75, 116, 170)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+41, 2280)-Net in Base 3 — Upper bound on s

There is no (75, 116, 2281)-net in base 3, because

1 times m-reduction [i] would yield (75, 115, 2281)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7 424378 188294 095525 650071 685859 644146 848770 204096 234577 > 3¹¹⁵ [i]