MinT - Best Known (123−80, 123, s)-Nets in Base 9

Best Known (123−80, 123, s)-Nets in Base 9

(123−80, 123, 81)-Net over F₉ — Constructive and digital

Digital (43, 123, 81)-net over F₉, using

t-expansion [i] based on digital (32, 123, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(123−80, 123, 147)-Net over F₉ — Digital

Digital (43, 123, 147)-net over F₉, using

net from sequence [i] based on digital (43, 146)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
  - a curve from the manYPoints database [i]

(123−80, 123, 1669)-Net in Base 9 — Upper bound on s

There is no (43, 123, 1670)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2358 069816 967406 506073 447835 750437 041759 829099 464146 919644 766064 553496 187841 976454 462759 625162 513258 305629 127567 582849 > 9¹²³ [i]