MinT - Best Known (74, 74+41, s)-Nets in Base 3

Best Known (74, 74+41, s)-Nets in Base 3

(74, 74+41, 128)-Net over F₃ — Constructive and digital

Digital (74, 115, 128)-net over F₃, using

7 times m-reduction [i] based on digital (74, 122, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 61, 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]

(74, 74+41, 165)-Net over F₃ — Digital

Digital (74, 115, 165)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+41, 2157)-Net in Base 3 — Upper bound on s

There is no (74, 115, 2158)-net in base 3, because

1 times m-reduction [i] would yield (74, 114, 2158)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 473708 284835 623304 511368 079419 821369 664448 197238 390697 > 3¹¹⁴ [i]