MinT - Best Known (132−87, 132, s)-Nets in Base 9

Best Known (132−87, 132, s)-Nets in Base 9

(132−87, 132, 81)-Net over F₉ — Constructive and digital

Digital (45, 132, 81)-net over F₉, using

t-expansion [i] based on digital (32, 132, 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]

(132−87, 132, 147)-Net over F₉ — Digital

Digital (45, 132, 147)-net over F₉, using

t-expansion [i] based on digital (43, 132, 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]

(132−87, 132, 1677)-Net in Base 9 — Upper bound on s

There is no (45, 132, 1678)-net in base 9, because

1 times m-reduction [i] would yield (45, 131, 1678)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101793 730528 894894 514942 047850 852699 639626 467882 223898 327745 104527 709969 195882 185522 568886 752576 201374 071324 382511 682627 745425 > 9¹³¹ [i]