MinT - Best Known (125−59, 125, s)-Nets in Base 9

Best Known (125−59, 125, s)-Nets in Base 9

(125−59, 125, 232)-Net over F₉ — Constructive and digital

Digital (66, 125, 232)-net over F₉, using

3 times m-reduction [i] based on digital (66, 128, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 64, 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]

(125−59, 125, 304)-Net over F₉ — Digital

Digital (66, 125, 304)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−59, 125, 17530)-Net in Base 9 — Upper bound on s

There is no (66, 125, 17531)-net in base 9, because

1 times m-reduction [i] would yield (66, 124, 17531)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21189 306867 236197 835921 526247 944355 018788 106004 300779 768656 316984 395411 265545 940371 505034 043045 508582 013041 757227 245177 > 9¹²⁴ [i]