MinT - Best Known (91, 91+63, s)-Nets in Base 3

Best Known (91, 91+63, s)-Nets in Base 3

(91, 91+63, 128)-Net over F₃ — Constructive and digital

Digital (91, 154, 128)-net over F₃, using

2 times m-reduction [i] based on digital (91, 156, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 78, 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]

(91, 91+63, 140)-Net over F₃ — Digital

Digital (91, 154, 140)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+63, 1375)-Net in Base 3 — Upper bound on s

There is no (91, 154, 1376)-net in base 3, because

1 times m-reduction [i] would yield (91, 153, 1376)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10 153726 220319 338404 052783 790075 282278 994134 874106 393224 829071 039513 694337 > 3¹⁵³ [i]