MinT - Best Known (18, 18+89, s)-Nets in Base 9

Best Known (18, 18+89, s)-Nets in Base 9

(18, 18+89, 74)-Net over F₉ — Constructive and digital

Digital (18, 107, 74)-net over F₉, using

t-expansion [i] based on digital (17, 107, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(18, 18+89, 402)-Net in Base 9 — Upper bound on s

There is no (18, 107, 403)-net in base 9, because

1 times m-reduction [i] would yield (18, 106, 403)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 145340 077504 189136 588806 179995 271340 041610 252744 995308 860808 771558 530074 358407 009136 157439 150773 571873 > 9¹⁰⁶ [i]