MinT - Best Known (150−86, 150, s)-Nets in Base 9

Best Known (150−86, 150, s)-Nets in Base 9

(150−86, 150, 165)-Net over F₉ — Constructive and digital

Digital (64, 150, 165)-net over F₉, using

net from sequence [i] based on digital (64, 164)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 64 and N(F) ≥ 165, using
  - T₄ from the second tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(150−86, 150, 192)-Net over F₉ — Digital

Digital (64, 150, 192)-net over F₉, using

t-expansion [i] based on digital (61, 150, 192)-net over F₉, using
- net from sequence [i] based on digital (61, 191)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 61 and N(F) ≥ 192, using
    - Drinfeld modules of rank 1 [i]

(150−86, 150, 4472)-Net in Base 9 — Upper bound on s

There is no (64, 150, 4473)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 137113 194947 808095 570228 405041 779796 763132 075083 040133 488989 635103 735023 919537 884586 161050 166866 980471 081328 302466 596307 848853 465694 786141 573465 > 9¹⁵⁰ [i]