MinT - Best Known (88, 88+59, s)-Nets in Base 9

Best Known (88, 88+59, s)-Nets in Base 9

(88, 88+59, 448)-Net over F₉ — Constructive and digital

Digital (88, 147, 448)-net over F₉, using

3 times m-reduction [i] based on digital (88, 150, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 75, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

(88, 88+59, 738)-Net over F₉ — Digital

Digital (88, 147, 738)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(88, 88+59, 92910)-Net in Base 9 — Upper bound on s

There is no (88, 147, 92911)-net in base 9, because

1 times m-reduction [i] would yield (88, 146, 92911)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 864428 546593 557132 517355 683674 385135 787281 208551 819644 706610 820988 160589 059103 007915 620204 916710 095722 616233 970501 659358 826348 620296 090777 > 9¹⁴⁶ [i]