MinT - Best Known (46, 46+101, s)-Nets in Base 9

Best Known (46, 46+101, s)-Nets in Base 9

(46, 46+101, 81)-Net over F₉ — Constructive and digital

Digital (46, 147, 81)-net over F₉, using

t-expansion [i] based on digital (32, 147, 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]

(46, 46+101, 162)-Net over F₉ — Digital

Digital (46, 147, 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]

(46, 46+101, 1458)-Net in Base 9 — Upper bound on s

There is no (46, 147, 1459)-net in base 9, because

1 times m-reduction [i] would yield (46, 146, 1459)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21 106276 948482 880848 951111 302355 760747 620333 125694 645887 488333 698631 783154 604426 433478 477571 765882 411479 322274 941131 732020 545076 856490 688305 > 9¹⁴⁶ [i]