MinT - Best Known (59, 59+91, s)-Nets in Base 9

Best Known (59, 59+91, s)-Nets in Base 9

(59, 59+91, 81)-Net over F₉ — Constructive and digital

Digital (59, 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]

(59, 59+91, 88)-Net in Base 9 — Constructive

(59, 150, 88)-net in base 9, using

base change [i] based on digital (9, 100, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(59, 59+91, 182)-Net over F₉ — Digital

Digital (59, 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]

(59, 59+91, 3154)-Net in Base 9 — Upper bound on s

There is no (59, 150, 3155)-net in base 9, because

1 times m-reduction [i] would yield (59, 149, 3155)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15351 607591 017841 175527 963807 486660 937215 632776 263885 216615 397916 362693 656743 681451 784181 945818 806590 197580 510487 997467 928639 714373 727454 043577 > 9¹⁴⁹ [i]