MinT - Best Known (71, 71+65, s)-Nets in Base 9

Best Known (71, 71+65, s)-Nets in Base 9

(71, 71+65, 232)-Net over F₉ — Constructive and digital

Digital (71, 136, 232)-net over F₉, using

2 times m-reduction [i] based on digital (71, 138, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 69, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(71, 71+65, 310)-Net over F₉ — Digital

Digital (71, 136, 310)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+65, 16943)-Net in Base 9 — Upper bound on s

There is no (71, 136, 16944)-net in base 9, because

1 times m-reduction [i] would yield (71, 135, 16944)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 665 575354 232590 779297 961965 794102 586711 056341 643491 332442 300680 511206 501921 236941 353905 445798 557885 087000 986094 080432 511499 751425 > 9¹³⁵ [i]