MinT - Best Known (198−49, 198, s)-Nets in Base 3

Best Known (198−49, 198, s)-Nets in Base 3

(198−49, 198, 328)-Net over F₃ — Constructive and digital

Digital (149, 198, 328)-net over F₃, using

3² times duplication [i] based on digital (147, 196, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 49, 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]

(198−49, 198, 877)-Net over F₃ — Digital

Digital (149, 198, 877)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−49, 198, 40406)-Net in Base 3 — Upper bound on s

There is no (149, 198, 40407)-net in base 3, because

1 times m-reduction [i] would yield (149, 197, 40407)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9840 823609 269191 276613 708598 398653 368503 310695 977161 974859 943550 976424 867562 986128 772691 287889 > 3¹⁹⁷ [i]