MinT - Best Known (53, 53+91, s)-Nets in Base 9

Best Known (53, 53+91, s)-Nets in Base 9

(53, 53+91, 81)-Net over F₉ — Constructive and digital

Digital (53, 144, 81)-net over F₉, using

t-expansion [i] based on digital (32, 144, 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]

(53, 53+91, 182)-Net over F₉ — Digital

Digital (53, 144, 182)-net over F₉, using

t-expansion [i] based on digital (50, 144, 182)-net over F₉, using
- net from sequence [i] based on digital (50, 181)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
    - a curve from the manYPoints database [i]

(53, 53+91, 2346)-Net in Base 9 — Upper bound on s

There is no (53, 144, 2347)-net in base 9, because

1 times m-reduction [i] would yield (53, 143, 2347)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28989 646977 287759 637557 738271 339967 187054 955496 621843 809478 394396 763153 434082 887097 275143 179132 754297 336595 106020 863490 337092 259252 794233 > 9¹⁴³ [i]