MinT - Best Known (171, 171+59, s)-Nets in Base 3

Best Known (171, 171+59, s)-Nets in Base 3

(171, 171+59, 288)-Net over F₃ — Constructive and digital

Digital (171, 230, 288)-net over F₃, using

10 times m-reduction [i] based on digital (171, 240, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 80, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(171, 171+59, 863)-Net over F₃ — Digital

Digital (171, 230, 863)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(171, 171+59, 34146)-Net in Base 3 — Upper bound on s

There is no (171, 230, 34147)-net in base 3, because

1 times m-reduction [i] would yield (171, 229, 34147)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 18 241427 978853 516217 087406 015792 038439 075175 881505 124237 957070 318099 984462 030611 195989 546541 589329 181136 593871 > 3²²⁹ [i]