MinT - Best Known (174, 174+57, s)-Nets in Base 3

Best Known (174, 174+57, s)-Nets in Base 3

(174, 174+57, 328)-Net over F₃ — Constructive and digital

Digital (174, 231, 328)-net over F₃, using

1 times m-reduction [i] based on digital (174, 232, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 58, 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]

(174, 174+57, 1008)-Net over F₃ — Digital

Digital (174, 231, 1008)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(174, 174+57, 46873)-Net in Base 3 — Upper bound on s

There is no (174, 231, 46874)-net in base 3, because

1 times m-reduction [i] would yield (174, 230, 46874)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 692253 683421 165618 151483 977005 692384 356576 266931 682231 923086 315597 541640 180103 622740 161644 983788 244298 449945 > 3²³⁰ [i]