MinT - Best Known (114−41, 114, s)-Nets in Base 9

Best Known (114−41, 114, s)-Nets in Base 9

(114−41, 114, 740)-Net over F₉ — Constructive and digital

Digital (73, 114, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 57, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(114−41, 114, 1053)-Net over F₉ — Digital

Digital (73, 114, 1053)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(114−41, 114, 255661)-Net in Base 9 — Upper bound on s

There is no (73, 114, 255662)-net in base 9, because

1 times m-reduction [i] would yield (73, 113, 255662)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 675159 584378 264713 844774 879550 851685 241638 382681 239483 178163 246959 183575 216643 381341 119216 341201 539685 113921 > 9¹¹³ [i]