MinT - Best Known (57, 57+93, s)-Nets in Base 9

Best Known (57, 57+93, s)-Nets in Base 9

(57, 57+93, 81)-Net over F₉ — Constructive and digital

Digital (57, 150, 81)-net over F₉, using

t-expansion [i] based on digital (32, 150, 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]

(57, 57+93, 82)-Net in Base 9 — Constructive

(57, 150, 82)-net in base 9, using

base change [i] based on digital (7, 100, 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]

(57, 57+93, 182)-Net over F₉ — Digital

Digital (57, 150, 182)-net over F₉, using

t-expansion [i] based on digital (50, 150, 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]

(57, 57+93, 2745)-Net in Base 9 — Upper bound on s

There is no (57, 150, 2746)-net in base 9, because

1 times m-reduction [i] would yield (57, 149, 2746)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15334 265383 071635 744739 538183 424236 387174 386216 476057 944513 554147 255773 121261 974664 209211 346811 130687 754152 005044 535826 624977 532660 009719 631009 > 9¹⁴⁹ [i]