MinT - Best Known (144−99, 144, s)-Nets in Base 9

Best Known (144−99, 144, s)-Nets in Base 9

(144−99, 144, 81)-Net over F₉ — Constructive and digital

Digital (45, 144, 81)-net over F₉, using

t-expansion [i] based on digital (32, 144, 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]

(144−99, 144, 147)-Net over F₉ — Digital

Digital (45, 144, 147)-net over F₉, using

t-expansion [i] based on digital (43, 144, 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]

(144−99, 144, 1425)-Net in Base 9 — Upper bound on s

There is no (45, 144, 1426)-net in base 9, because

1 times m-reduction [i] would yield (45, 143, 1426)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 28933 217962 647602 231214 106989 542797 004775 275805 986976 742555 388718 871768 559320 041662 186688 147325 775373 495513 071662 919554 383535 698101 561745 > 9¹⁴³ [i]