MinT - Best Known (64, 64+30, s)-Nets in Base 9

Best Known (64, 64+30, s)-Nets in Base 9

(64, 64+30, 740)-Net over F₉ — Constructive and digital

Digital (64, 94, 740)-net over F₉, using

2 times m-reduction [i] based on digital (64, 96, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 48, 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]

(64, 64+30, 1822)-Net over F₉ — Digital

Digital (64, 94, 1822)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+30, 766639)-Net in Base 9 — Upper bound on s

There is no (64, 94, 766640)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 499801 706051 519323 920174 681087 262403 367099 073823 067910 878549 335344 074463 334874 747155 368065 > 9⁹⁴ [i]