MinT - Best Known (97−77, 97, s)-Nets in Base 9

Best Known (97−77, 97, s)-Nets in Base 9

(97−77, 97, 74)-Net over F₉ — Constructive and digital

Digital (20, 97, 74)-net over F₉, using

t-expansion [i] based on digital (17, 97, 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]

(97−77, 97, 84)-Net over F₉ — Digital

Digital (20, 97, 84)-net over F₉, using

t-expansion [i] based on digital (19, 97, 84)-net over F₉, using
- net from sequence [i] based on digital (19, 83)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 19 and N(F) ≥ 84, using
    - Drinfeld modules of rank 1 [i]

(97−77, 97, 460)-Net in Base 9 — Upper bound on s

There is no (20, 97, 461)-net in base 9, because

1 times m-reduction [i] would yield (20, 96, 461)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 41 739964 959817 625253 448892 973348 419808 053475 922930 991243 430913 508630 185962 749347 299978 661041 > 9⁹⁶ [i]