MinT - Best Known (147−91, 147, s)-Nets in Base 9

Best Known (147−91, 147, s)-Nets in Base 9

(147−91, 147, 81)-Net over F₉ — Constructive and digital

Digital (56, 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]

(147−91, 147, 82)-Net in Base 9 — Constructive

(56, 147, 82)-net in base 9, using

base change [i] based on digital (7, 98, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(147−91, 147, 182)-Net over F₉ — Digital

Digital (56, 147, 182)-net over F₉, using

t-expansion [i] based on digital (50, 147, 182)-net over F₉, using
- net from sequence [i] based on digital (50, 181)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
    - a curve from the manYPoints database [i]

(147−91, 147, 2720)-Net in Base 9 — Upper bound on s

There is no (56, 147, 2721)-net in base 9, because

1 times m-reduction [i] would yield (56, 146, 2721)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 934313 284793 754313 703523 030332 235104 589812 464907 851861 833706 337863 289891 817850 100782 353819 192105 966201 445126 476577 968179 943382 491643 198953 > 9¹⁴⁶ [i]