MinT - Best Known (207−67, 207, s)-Nets in Base 3

Best Known (207−67, 207, s)-Nets in Base 3

(207−67, 207, 162)-Net over F₃ — Constructive and digital

Digital (140, 207, 162)-net over F₃, using

9 times m-reduction [i] based on digital (140, 216, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 108, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(207−67, 207, 360)-Net over F₃ — Digital

Digital (140, 207, 360)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−67, 207, 6229)-Net in Base 3 — Upper bound on s

There is no (140, 207, 6230)-net in base 3, because

1 times m-reduction [i] would yield (140, 206, 6230)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 194 007602 759827 522090 703378 802882 722577 046830 571743 911422 826524 068524 410304 770909 218320 722123 372653 > 3²⁰⁶ [i]