MinT - Best Known (150−96, 150, s)-Nets in Base 9

Best Known (150−96, 150, s)-Nets in Base 9

(150−96, 150, 81)-Net over F₉ — Constructive and digital

Digital (54, 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]

(150−96, 150, 182)-Net over F₉ — Digital

Digital (54, 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]

(150−96, 150, 2218)-Net in Base 9 — Upper bound on s

There is no (54, 150, 2219)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 139387 914632 284784 656604 709821 110964 203676 327675 042332 534600 798078 560429 851288 937956 218137 514831 353507 557451 661218 842339 859860 999915 461962 470529 > 9¹⁵⁰ [i]