MinT - Best Known (72, 72+59, s)-Nets in Base 9

Best Known (72, 72+59, s)-Nets in Base 9

(72, 72+59, 320)-Net over F₉ — Constructive and digital

Digital (72, 131, 320)-net over F₉, using

3 times m-reduction [i] based on digital (72, 134, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 67, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(72, 72+59, 388)-Net over F₉ — Digital

Digital (72, 131, 388)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+59, 27630)-Net in Base 9 — Upper bound on s

There is no (72, 131, 27631)-net in base 9, because

1 times m-reduction [i] would yield (72, 130, 27631)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11261 646553 907083 629927 501220 561585 162349 315492 015517 603607 517553 127352 294609 521215 686465 045121 675735 470498 214455 972642 036889 > 9¹³⁰ [i]