MinT - Best Known (111, 111+37, s)-Nets in Base 3

Best Known (111, 111+37, s)-Nets in Base 3

(111, 111+37, 328)-Net over F₃ — Constructive and digital

Digital (111, 148, 328)-net over F₃, using

trace code for nets [i] based on digital (0, 37, 82)-net over F₈₁, using
- net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
    - the rational function field F₈₁(x) [i]
  - Niederreiter sequence [i]

(111, 111+37, 671)-Net over F₃ — Digital

Digital (111, 148, 671)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(111, 111+37, 29739)-Net in Base 3 — Upper bound on s

There is no (111, 148, 29740)-net in base 3, because

1 times m-reduction [i] would yield (111, 147, 29740)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13706 725995 292098 378478 798140 154113 834624 716691 444320 702372 786309 612841 > 3¹⁴⁷ [i]