MinT - Best Known (72, 72+58, s)-Nets in Base 9

Best Known (72, 72+58, s)-Nets in Base 9

(72, 72+58, 344)-Net over F₉ — Constructive and digital

Digital (72, 130, 344)-net over F₉, using

trace code for nets [i] based on digital (7, 65, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(72, 72+58, 402)-Net over F₉ — Digital

Digital (72, 130, 402)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+58, 27630)-Net in Base 9 — Upper bound on s

There is no (72, 130, 27631)-net in base 9, because

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]