MinT - Best Known (113−69, 113, s)-Nets in Base 9

Best Known (113−69, 113, s)-Nets in Base 9

(113−69, 113, 81)-Net over F₉ — Constructive and digital

Digital (44, 113, 81)-net over F₉, using

t-expansion [i] based on digital (32, 113, 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]

(113−69, 113, 147)-Net over F₉ — Digital

Digital (44, 113, 147)-net over F₉, using

t-expansion [i] based on digital (43, 113, 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]

(113−69, 113, 2333)-Net in Base 9 — Upper bound on s

There is no (44, 113, 2334)-net in base 9, because

1 times m-reduction [i] would yield (44, 112, 2334)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 75976 847155 582928 147141 036609 965889 736103 777363 172475 702869 423570 381455 303167 826617 422208 456540 029432 303649 > 9¹¹² [i]