MinT - Best Known (23, 23+100, s)-Nets in Base 9

Best Known (23, 23+100, s)-Nets in Base 9

(23, 23+100, 78)-Net over F₉ — Constructive and digital

Digital (23, 123, 78)-net over F₉, using

t-expansion [i] based on digital (22, 123, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(23, 23+100, 92)-Net over F₉ — Digital

Digital (23, 123, 92)-net over F₉, using

net from sequence [i] based on digital (23, 91)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 23 and N(F) ≥ 92, using
  - Drinfeld modules of rank 1 [i]

(23, 23+100, 511)-Net in Base 9 — Upper bound on s

There is no (23, 123, 512)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2406 913189 905145 033101 924971 728387 426748 419178 147131 086993 322583 973879 735287 093101 775763 098742 584630 741632 178747 432961 > 9¹²³ [i]