MinT - Best Known (131−87, 131, s)-Nets in Base 9

Best Known (131−87, 131, s)-Nets in Base 9

(131−87, 131, 81)-Net over F₉ — Constructive and digital

Digital (44, 131, 81)-net over F₉, using

t-expansion [i] based on digital (32, 131, 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]

(131−87, 131, 147)-Net over F₉ — Digital

Digital (44, 131, 147)-net over F₉, using

t-expansion [i] based on digital (43, 131, 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]

(131−87, 131, 1592)-Net in Base 9 — Upper bound on s

There is no (44, 131, 1593)-net in base 9, because

1 times m-reduction [i] would yield (44, 130, 1593)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11277 657005 283003 817203 350309 328357 622117 045756 991449 914595 481107 740564 660347 090741 068067 413283 012943 914597 039049 177057 651545 > 9¹³⁰ [i]