MinT - Best Known (23, 142, s)-Nets in Base 9

Best Known (23, 142, s)-Nets in Base 9

(23, 142, 78)-Net over F₉ — Constructive and digital

Digital (23, 142, 78)-net over F₉, using

t-expansion [i] based on digital (22, 142, 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, 142, 92)-Net over F₉ — Digital

Digital (23, 142, 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, 142, 508)-Net in Base 9 — Upper bound on s

There is no (23, 142, 509)-net in base 9, because

1 times m-reduction [i] would yield (23, 141, 509)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 374 003787 256656 144856 433096 825836 885979 324024 522560 307923 930535 033313 829275 082030 475126 693904 284650 274913 280941 971520 748204 176469 259193 > 9¹⁴¹ [i]