MinT - Best Known (185−77, 185, s)-Nets in Base 3

Best Known (185−77, 185, s)-Nets in Base 3

(185−77, 185, 128)-Net over F₃ — Constructive and digital

Digital (108, 185, 128)-net over F₃, using

5 times m-reduction [i] based on digital (108, 190, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 95, 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]

(185−77, 185, 156)-Net over F₃ — Digital

Digital (108, 185, 156)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−77, 185, 1497)-Net in Base 3 — Upper bound on s

There is no (108, 185, 1498)-net in base 3, because

1 times m-reduction [i] would yield (108, 184, 1498)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6223 806273 218627 596531 575280 170841 602137 263128 647909 074464 884010 004445 885754 448469 581581 > 3¹⁸⁴ [i]