MinT - Best Known (45, 45+97, s)-Nets in Base 9

Best Known (45, 45+97, s)-Nets in Base 9

(45, 45+97, 81)-Net over F₉ — Constructive and digital

Digital (45, 142, 81)-net over F₉, using

t-expansion [i] based on digital (32, 142, 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]

(45, 45+97, 147)-Net over F₉ — Digital

Digital (45, 142, 147)-net over F₉, using

t-expansion [i] based on digital (43, 142, 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]

(45, 45+97, 1459)-Net in Base 9 — Upper bound on s

There is no (45, 142, 1460)-net in base 9, because

1 times m-reduction [i] would yield (45, 141, 1460)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 361 394318 201016 267926 133450 402445 175547 092792 551943 502657 556904 094200 710919 717378 381099 155215 036440 672338 543845 446553 537723 596015 223297 > 9¹⁴¹ [i]