MinT - Best Known (44, 115, s)-Nets in Base 9

Best Known (44, 115, s)-Nets in Base 9

(44, 115, 81)-Net over F₉ — Constructive and digital

Digital (44, 115, 81)-net over F₉, using

t-expansion [i] based on digital (32, 115, 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]

(44, 115, 147)-Net over F₉ — Digital

Digital (44, 115, 147)-net over F₉, using

t-expansion [i] based on digital (43, 115, 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]

(44, 115, 2208)-Net in Base 9 — Upper bound on s

There is no (44, 115, 2209)-net in base 9, because

1 times m-reduction [i] would yield (44, 114, 2209)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 6 119740 918980 174107 349033 450173 226947 380242 995731 235880 232486 511608 251578 174714 070169 529769 588520 723676 216025 > 9¹¹⁴ [i]