MinT - Best Known (134−102, 134, s)-Nets in Base 9

Best Known (134−102, 134, s)-Nets in Base 9

(134−102, 134, 81)-Net over F₉ — Constructive and digital

Digital (32, 134, 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]

(134−102, 134, 120)-Net over F₉ — Digital

Digital (32, 134, 120)-net over F₉, using

t-expansion [i] based on digital (31, 134, 120)-net over F₉, using
- net from sequence [i] based on digital (31, 119)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 31 and N(F) ≥ 120, using
    - a curve from the manYPoints database [i]

(134−102, 134, 766)-Net in Base 9 — Upper bound on s

There is no (32, 134, 767)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 74 071357 066186 843061 633001 319995 502801 459145 806761 718498 475501 018393 191615 294053 249012 231760 039258 800385 592543 929212 288666 281577 > 9¹³⁴ [i]