MinT - Best Known (123−82, 123, s)-Nets in Base 9

Best Known (123−82, 123, s)-Nets in Base 9

(123−82, 123, 81)-Net over F₉ — Constructive and digital

Digital (41, 123, 81)-net over F₉, using

t-expansion [i] based on digital (32, 123, 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]

(123−82, 123, 140)-Net over F₉ — Digital

Digital (41, 123, 140)-net over F₉, using

t-expansion [i] based on digital (39, 123, 140)-net over F₉, using
- net from sequence [i] based on digital (39, 139)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
    - a curve from the manYPoints database [i]

(123−82, 123, 1445)-Net in Base 9 — Upper bound on s

There is no (41, 123, 1446)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2367 983220 914917 535320 706438 485077 682275 680813 646928 494787 277676 503300 916531 919216 951250 778300 468365 955715 510138 985905 > 9¹²³ [i]