MinT - Best Known (71, 71+32, s)-Nets in Base 9

Best Known (71, 71+32, s)-Nets in Base 9

(71, 71+32, 740)-Net over F₉ — Constructive and digital

Digital (71, 103, 740)-net over F₉, using

7 times m-reduction [i] based on digital (71, 110, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 55, 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]

(71, 71+32, 2314)-Net over F₉ — Digital

Digital (71, 103, 2314)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+32, 1181357)-Net in Base 9 — Upper bound on s

There is no (71, 103, 1181358)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 193 633503 073396 095160 876302 876503 009035 890070 878674 930804 232114 969144 235435 881687 132634 068561 855745 > 9¹⁰³ [i]