MinT - Best Known (103−82, 103, s)-Nets in Base 9

Best Known (103−82, 103, s)-Nets in Base 9

(103−82, 103, 74)-Net over F₉ — Constructive and digital

Digital (21, 103, 74)-net over F₉, using

t-expansion [i] based on digital (17, 103, 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]

(103−82, 103, 88)-Net over F₉ — Digital

Digital (21, 103, 88)-net over F₉, using

net from sequence [i] based on digital (21, 87)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 21 and N(F) ≥ 88, using
  - a curve from the manYPoints database [i]

(103−82, 103, 478)-Net in Base 9 — Upper bound on s

There is no (21, 103, 479)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 196 598623 203485 534801 833391 290218 425303 050284 294218 279193 000768 968751 178835 343274 229207 883590 317497 > 9¹⁰³ [i]