MinT - Best Known (205−51, 205, s)-Nets in Base 3

Best Known (205−51, 205, s)-Nets in Base 3

(205−51, 205, 328)-Net over F₃ — Constructive and digital

Digital (154, 205, 328)-net over F₃, using

3¹ times duplication [i] based on digital (153, 204, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 51, 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]

(205−51, 205, 884)-Net over F₃ — Digital

Digital (154, 205, 884)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−51, 205, 39777)-Net in Base 3 — Upper bound on s

There is no (154, 205, 39778)-net in base 3, because

1 times m-reduction [i] would yield (154, 204, 39778)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21 520941 585674 053727 884365 312250 429612 793162 029531 844029 351083 703142 807843 656517 770345 186225 445205 > 3²⁰⁴ [i]