MinT - Best Known (80, 80+67, s)-Nets in Base 9

Best Known (80, 80+67, s)-Nets in Base 9

(80, 80+67, 320)-Net over F₉ — Constructive and digital

Digital (80, 147, 320)-net over F₉, using

3 times m-reduction [i] based on digital (80, 150, 320)-net over F₉, using
- trace code for nets [i] based on digital (5, 75, 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]

(80, 80+67, 406)-Net over F₉ — Digital

Digital (80, 147, 406)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+67, 27399)-Net in Base 9 — Upper bound on s

There is no (80, 147, 27400)-net in base 9, because

1 times m-reduction [i] would yield (80, 146, 27400)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 872419 946316 130492 117983 029432 375340 748008 196555 820798 819818 648828 872416 474033 830522 436388 047685 624861 190196 025545 269206 406398 674344 669249 > 9¹⁴⁶ [i]