MinT - Best Known (91, 91+61, s)-Nets in Base 3

Best Known (91, 91+61, s)-Nets in Base 3

(91, 91+61, 128)-Net over F₃ — Constructive and digital

Digital (91, 152, 128)-net over F₃, using

4 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+61, 147)-Net over F₃ — Digital

Digital (91, 152, 147)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(91, 91+61, 1488)-Net in Base 3 — Upper bound on s

There is no (91, 152, 1489)-net in base 3, because

1 times m-reduction [i] would yield (91, 151, 1489)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 115964 478299 787906 459004 735928 537233 236796 039859 723612 140971 149875 877337 > 3¹⁵¹ [i]