MinT - Best Known (113−91, 113, s)-Nets in Base 9

Best Known (113−91, 113, s)-Nets in Base 9

(113−91, 113, 78)-Net over F₉ — Constructive and digital

Digital (22, 113, 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]

(113−91, 113, 88)-Net over F₉ — Digital

Digital (22, 113, 88)-net over F₉, using

t-expansion [i] based on digital (21, 113, 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]

(113−91, 113, 495)-Net in Base 9 — Upper bound on s

There is no (22, 113, 496)-net in base 9, because

1 times m-reduction [i] would yield (22, 112, 496)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 79712 399953 793623 229311 517428 202754 398596 954391 115322 583356 297432 656485 577135 510369 252090 014214 401400 913281 > 9¹¹² [i]