MinT - Best Known (98−51, 98, s)-Nets in Base 3

Best Known (98−51, 98, s)-Nets in Base 3

(98−51, 98, 48)-Net over F₃ — Constructive and digital

Digital (47, 98, 48)-net over F₃, using

t-expansion [i] based on digital (45, 98, 48)-net over F₃, using
- net from sequence [i] based on digital (45, 47)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 45 and N(F) ≥ 48, using
    - an explicitly constructive algebraic function field [i]

(98−51, 98, 56)-Net over F₃ — Digital

Digital (47, 98, 56)-net over F₃, using

t-expansion [i] based on digital (40, 98, 56)-net over F₃, using
- net from sequence [i] based on digital (40, 55)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 40 and N(F) ≥ 56, using
    - a curve from the manYPoints database [i]

(98−51, 98, 337)-Net in Base 3 — Upper bound on s

There is no (47, 98, 338)-net in base 3, because

1 times m-reduction [i] would yield (47, 97, 338)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 19849 552100 860272 249710 286291 632769 132372 395829 > 3⁹⁷ [i]