MinT - Best Known (63−28, 63, s)-Nets in Base 9

Best Known (63−28, 63, s)-Nets in Base 9

(63−28, 63, 232)-Net over F₉ — Constructive and digital

Digital (35, 63, 232)-net over F₉, using

3 times m-reduction [i] based on digital (35, 66, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 33, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(63−28, 63, 272)-Net over F₉ — Digital

Digital (35, 63, 272)-net over F₉, using

1 times m-reduction [i] based on digital (35, 64, 272)-net over F₉, using
- trace code for nets [i] based on digital (3, 32, 136)-net over F₈₁, using
  - net from sequence [i] based on digital (3, 135)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
      - a curve from the manYPoints database [i]

(63−28, 63, 14866)-Net in Base 9 — Upper bound on s

There is no (35, 63, 14867)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 310239 592607 583875 909020 035747 693774 838210 714991 027313 732305 > 9⁶³ [i]