MinT - Best Known (98, 98+57, s)-Nets in Base 3

Best Known (98, 98+57, s)-Nets in Base 3

(98, 98+57, 148)-Net over F₃ — Constructive and digital

Digital (98, 155, 148)-net over F₃, using

7 times m-reduction [i] based on digital (98, 162, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 81, 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]

(98, 98+57, 191)-Net over F₃ — Digital

Digital (98, 155, 191)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+57, 2350)-Net in Base 3 — Upper bound on s

There is no (98, 155, 2351)-net in base 3, because

1 times m-reduction [i] would yield (98, 154, 2351)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30 235158 173016 543763 177225 799712 321737 861304 866518 104476 088498 882500 261577 > 3¹⁵⁴ [i]