MinT - Best Known (117−72, 117, s)-Nets in Base 9

Best Known (117−72, 117, s)-Nets in Base 9

(117−72, 117, 81)-Net over F₉ — Constructive and digital

Digital (45, 117, 81)-net over F₉, using

t-expansion [i] based on digital (32, 117, 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]

(117−72, 117, 147)-Net over F₉ — Digital

Digital (45, 117, 147)-net over F₉, using

t-expansion [i] based on digital (43, 117, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(117−72, 117, 2231)-Net in Base 9 — Upper bound on s

There is no (45, 117, 2232)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4432 086216 454233 972534 392775 763420 164007 106406 431956 317190 069362 891867 225750 827001 184681 130440 077331 363024 713985 > 9¹¹⁷ [i]