MinT - Best Known (65, 65+30, s)-Nets in Base 9

Best Known (65, 65+30, s)-Nets in Base 9

(65, 65+30, 740)-Net over F₉ — Constructive and digital

Digital (65, 95, 740)-net over F₉, using

3 times m-reduction [i] based on digital (65, 98, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 49, 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]

(65, 65+30, 1964)-Net over F₉ — Digital

Digital (65, 95, 1964)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+30, 887581)-Net in Base 9 — Upper bound on s

There is no (65, 95, 887582)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 498240 018495 988725 755713 546690 150092 410977 502323 227644 013366 645336 383625 293184 201650 373713 > 9⁹⁵ [i]