MinT - Best Known (175−43, 175, s)-Nets in Base 3

Best Known (175−43, 175, s)-Nets in Base 3

(175−43, 175, 328)-Net over F₃ — Constructive and digital

Digital (132, 175, 328)-net over F₃, using

1 times m-reduction [i] based on digital (132, 176, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 44, 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]

(175−43, 175, 819)-Net over F₃ — Digital

Digital (132, 175, 819)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−43, 175, 38951)-Net in Base 3 — Upper bound on s

There is no (132, 175, 38952)-net in base 3, because

1 times m-reduction [i] would yield (132, 174, 38952)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 104522 195114 039259 974730 874855 526427 962351 705978 369102 822682 832174 610770 253352 257745 > 3¹⁷⁴ [i]