MinT - Best Known (47, 47+101, s)-Nets in Base 9

Best Known (47, 47+101, s)-Nets in Base 9

(47, 47+101, 81)-Net over F₉ — Constructive and digital

Digital (47, 148, 81)-net over F₉, using

t-expansion [i] based on digital (32, 148, 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]

(47, 47+101, 162)-Net over F₉ — Digital

Digital (47, 148, 162)-net over F₉, using

t-expansion [i] based on digital (46, 148, 162)-net over F₉, using
- net from sequence [i] based on digital (46, 161)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
    - a curve from the manYPoints database [i]

(47, 47+101, 1525)-Net in Base 9 — Upper bound on s

There is no (47, 148, 1526)-net in base 9, because

1 times m-reduction [i] would yield (47, 147, 1526)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 190 506922 206206 419960 939165 986174 605656 380910 392276 618583 106227 777803 309116 363459 122877 079351 407358 196190 114177 599239 322612 785166 602292 651425 > 9¹⁴⁷ [i]