MinT - Best Known (50, 123, s)-Nets in Base 9

Best Known (50, 123, s)-Nets in Base 9

(50, 123, 81)-Net over F₉ — Constructive and digital

Digital (50, 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]

(50, 123, 88)-Net in Base 9 — Constructive

(50, 123, 88)-net in base 9, using

base change [i] based on digital (9, 82, 88)-net over F₂₇, using
- net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
    - a function field by SÃ©mirat [i]

(50, 123, 182)-Net over F₉ — Digital

Digital (50, 123, 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]

(50, 123, 3036)-Net in Base 9 — Upper bound on s

There is no (50, 123, 3037)-net in base 9, because

1 times m-reduction [i] would yield (50, 122, 3037)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 263 832353 731402 165468 342731 876347 773078 565064 365617 762775 072139 804548 101024 871212 892975 829932 581738 715947 671857 307937 > 9¹²² [i]