MinT - Best Known (81−66, 81, s)-Nets in Base 9

Best Known (81−66, 81, s)-Nets in Base 9

(81−66, 81, 64)-Net over F₉ — Constructive and digital

Digital (15, 81, 64)-net over F₉, using

t-expansion [i] based on digital (13, 81, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(81−66, 81, 342)-Net in Base 9 — Upper bound on s

There is no (15, 81, 343)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 214979 200063 242677 341958 084527 935359 043581 152636 022964 053142 184827 470719 463865 > 9⁸¹ [i]