MinT - Best Known (207−87, 207, s)-Nets in Base 3

Best Known (207−87, 207, s)-Nets in Base 3

(207−87, 207, 128)-Net over F₃ — Constructive and digital

Digital (120, 207, 128)-net over F₃, using

7 times m-reduction [i] based on digital (120, 214, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 107, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(207−87, 207, 168)-Net over F₃ — Digital

Digital (120, 207, 168)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(207−87, 207, 1587)-Net in Base 3 — Upper bound on s

There is no (120, 207, 1588)-net in base 3, because

1 times m-reduction [i] would yield (120, 206, 1588)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 193 961300 221701 127426 947182 559321 470731 175474 572509 917846 057365 226835 033005 300770 588104 585998 291889 > 3²⁰⁶ [i]