MinT - Best Known (99−29, 99, s)-Nets in Base 9

Best Known (99−29, 99, s)-Nets in Base 9

(99−29, 99, 740)-Net over F₉ — Constructive and digital

Digital (70, 99, 740)-net over F₉, using

9 times m-reduction [i] based on digital (70, 108, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 54, 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]

(99−29, 99, 3355)-Net over F₉ — Digital

Digital (70, 99, 3355)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(99−29, 99, 3614633)-Net in Base 9 — Upper bound on s

There is no (70, 99, 3614634)-net in base 9, because

1 times m-reduction [i] would yield (70, 98, 3614634)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 3279 185264 666541 219491 164348 343525 536276 725248 393376 948254 162575 100577 448540 775723 131919 628705 > 9⁹⁸ [i]