MinT - Best Known (97−79, 97, s)-Nets in Base 9

Best Known (97−79, 97, s)-Nets in Base 9

(97−79, 97, 74)-Net over F₉ — Constructive and digital

Digital (18, 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]

(97−79, 97, 406)-Net in Base 9 — Upper bound on s

There is no (18, 97, 407)-net in base 9, because

1 times m-reduction [i] would yield (18, 96, 407)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 43 216046 876356 780379 733340 901124 506449 302162 566497 399548 236979 487125 397765 588623 436289 392905 > 9⁹⁶ [i]