MinT - Best Known (146−111, 146, s)-Nets in Base 9

Best Known (146−111, 146, s)-Nets in Base 9

(146−111, 146, 81)-Net over F₉ — Constructive and digital

Digital (35, 146, 81)-net over F₉, using

t-expansion [i] based on digital (32, 146, 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]

(146−111, 146, 128)-Net over F₉ — Digital

Digital (35, 146, 128)-net over F₉, using

t-expansion [i] based on digital (33, 146, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(146−111, 146, 841)-Net in Base 9 — Upper bound on s

There is no (35, 146, 842)-net in base 9, because

1 times m-reduction [i] would yield (35, 145, 842)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 456475 634680 068001 198216 291294 101922 725346 192863 965189 400396 631234 259049 203428 356032 989934 426324 815002 139785 058570 806541 533830 424501 783025 > 9¹⁴⁵ [i]