MinT - Best Known (78, 78+38, s)-Nets in Base 9

Best Known (78, 78+38, s)-Nets in Base 9

(78, 78+38, 740)-Net over F₉ — Constructive and digital

Digital (78, 116, 740)-net over F₉, using

8 times m-reduction [i] based on digital (78, 124, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 62, 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]

(78, 78+38, 1815)-Net over F₉ — Digital

Digital (78, 116, 1815)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+38, 663773)-Net in Base 9 — Upper bound on s

There is no (78, 116, 663774)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 492 199356 038672 009016 672711 241347 080281 354056 420456 883495 502234 162657 894121 891585 537264 476544 793388 821975 683729 > 9¹¹⁶ [i]