MinT - Best Known (150−92, 150, s)-Nets in Base 9

Best Known (150−92, 150, s)-Nets in Base 9

(150−92, 150, 81)-Net over F₉ — Constructive and digital

Digital (58, 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]

(150−92, 150, 84)-Net in Base 9 — Constructive

(58, 150, 84)-net in base 9, using

base change [i] based on digital (8, 100, 84)-net over F₂₇, using
- net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
    - a function field by SÃ©mirat [i]

(150−92, 150, 182)-Net over F₉ — Digital

Digital (58, 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]

(150−92, 150, 2881)-Net in Base 9 — Upper bound on s

There is no (58, 150, 2882)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 138616 318751 962973 005700 231045 835920 650585 920514 356359 240445 239216 361664 616798 036028 143454 149754 189560 563144 762032 541053 771814 550152 587586 518817 > 9¹⁵⁰ [i]