MinT - Best Known (62, 116, s)-Nets in Base 9

Best Known (62, 116, s)-Nets in Base 9

(62, 116, 300)-Net over F₉ — Constructive and digital

Digital (62, 116, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 58, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(62, 116, 308)-Net over F₉ — Digital

Digital (62, 116, 308)-net over F₉, using

trace code for nets [i] based on digital (4, 58, 154)-net over F₈₁, using
- net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
    - a curve from the manYPoints database [i]

(62, 116, 17163)-Net in Base 9 — Upper bound on s

There is no (62, 116, 17164)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 492 407826 646805 310722 415541 514522 388056 392407 878997 468670 278812 259054 833277 614576 439960 522681 672069 409599 932065 > 9¹¹⁶ [i]