MinT - Best Known (215−91, 215, s)-Nets in Base 3

Best Known (215−91, 215, s)-Nets in Base 3

(215−91, 215, 128)-Net over F₃ — Constructive and digital

Digital (124, 215, 128)-net over F₃, using

7 times m-reduction [i] based on digital (124, 222, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 111, 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]

(215−91, 215, 170)-Net over F₃ — Digital

Digital (124, 215, 170)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(215−91, 215, 1593)-Net in Base 3 — Upper bound on s

There is no (124, 215, 1594)-net in base 3, because

1 times m-reduction [i] would yield (124, 214, 1594)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 296278 932986 353606 174795 894842 205852 137532 937295 699916 996022 326244 302642 283291 771209 044300 027465 343037 > 3²¹⁴ [i]