MinT - Best Known (129−41, 129, s)-Nets in Base 9

Best Known (129−41, 129, s)-Nets in Base 9

(129−41, 129, 740)-Net over F₉ — Constructive and digital

Digital (88, 129, 740)-net over F₉, using

15 times m-reduction [i] based on digital (88, 144, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 72, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(129−41, 129, 2376)-Net over F₉ — Digital

Digital (88, 129, 2376)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(129−41, 129, 1328508)-Net in Base 9 — Upper bound on s

There is no (88, 129, 1328509)-net in base 9, because

1 times m-reduction [i] would yield (88, 128, 1328509)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 139 009216 993401 934926 940333 713234 317766 684663 650839 272769 830409 149638 486268 379311 718999 643992 269198 792668 946448 354644 456609 > 9¹²⁸ [i]