MinT - Best Known (130−59, 130, s)-Nets in Base 9

Best Known (130−59, 130, s)-Nets in Base 9

(130−59, 130, 320)-Net over F₉ — Constructive and digital

Digital (71, 130, 320)-net over F₉, using

2 times m-reduction [i] based on digital (71, 132, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 66, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(130−59, 130, 380)-Net over F₉ — Digital

Digital (71, 130, 380)-net over F₉, using

trace code for nets [i] based on digital (6, 65, 190)-net over F₈₁, using
- net from sequence [i] based on digital (6, 189)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 6 and N(F) ≥ 190, using
    - a curve from the manYPoints database [i]

(130−59, 130, 25613)-Net in Base 9 — Upper bound on s

There is no (71, 130, 25614)-net in base 9, because

1 times m-reduction [i] would yield (71, 129, 25614)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1251 921546 240220 747834 242534 668653 803009 365285 641971 747281 256611 086426 367299 241177 009556 850211 874646 390018 213910 058093 432369 > 9¹²⁹ [i]