MinT - Best Known (149−105, 149, s)-Nets in Base 9

Best Known (149−105, 149, s)-Nets in Base 9

(149−105, 149, 81)-Net over F₉ — Constructive and digital

Digital (44, 149, 81)-net over F₉, using

t-expansion [i] based on digital (32, 149, 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]

(149−105, 149, 147)-Net over F₉ — Digital

Digital (44, 149, 147)-net over F₉, using

t-expansion [i] based on digital (43, 149, 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]

(149−105, 149, 1282)-Net in Base 9 — Upper bound on s

There is no (44, 149, 1283)-net in base 9, because

1 times m-reduction [i] would yield (44, 148, 1283)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1715 144646 541433 123538 979375 417245 198459 628913 842903 084828 249513 809824 906516 510137 615295 461715 168411 671227 853301 713840 722766 597683 771774 101985 > 9¹⁴⁸ [i]