MinT - Best Known (43−29, 43, s)-Nets in Base 9

Best Known (43−29, 43, s)-Nets in Base 9

(43−29, 43, 64)-Net over F₉ — Constructive and digital

Digital (14, 43, 64)-net over F₉, using

t-expansion [i] based on digital (13, 43, 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]

(43−29, 43, 542)-Net in Base 9 — Upper bound on s

There is no (14, 43, 543)-net in base 9, because

1 times m-reduction [i] would yield (14, 42, 543)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 12059 117756 120387 841249 487129 341575 840145 > 9⁴² [i]