MinT - Best Known (145−69, 145, s)-Nets in Base 9

Best Known (145−69, 145, s)-Nets in Base 9

(145−69, 145, 232)-Net over F₉ — Constructive and digital

Digital (76, 145, 232)-net over F₉, using

3 times m-reduction [i] based on digital (76, 148, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 74, 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]

(145−69, 145, 334)-Net over F₉ — Digital

Digital (76, 145, 334)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−69, 145, 18595)-Net in Base 9 — Upper bound on s

There is no (76, 145, 18596)-net in base 9, because

1 times m-reduction [i] would yield (76, 144, 18596)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 258000 777164 975587 428348 519126 698689 629828 232735 640612 399476 608356 376621 656151 548190 610993 456601 237347 970240 310041 927869 391029 289180 011713 > 9¹⁴⁴ [i]