MinT - Best Known (203−85, 203, s)-Nets in Base 3

Best Known (203−85, 203, s)-Nets in Base 3

(203−85, 203, 128)-Net over F₃ — Constructive and digital

Digital (118, 203, 128)-net over F₃, using

7 times m-reduction [i] based on digital (118, 210, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 105, 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]

(203−85, 203, 166)-Net over F₃ — Digital

Digital (118, 203, 166)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(203−85, 203, 1586)-Net in Base 3 — Upper bound on s

There is no (118, 203, 1587)-net in base 3, because

1 times m-reduction [i] would yield (118, 202, 1587)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 431028 156106 519553 773948 372466 907664 966869 178672 037233 254203 499214 202191 642299 136123 958625 263989 > 3²⁰² [i]