MinT - Best Known (125−79, 125, s)-Nets in Base 9

Best Known (125−79, 125, s)-Nets in Base 9

(125−79, 125, 81)-Net over F₉ — Constructive and digital

Digital (46, 125, 81)-net over F₉, using

t-expansion [i] based on digital (32, 125, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(125−79, 125, 162)-Net over F₉ — Digital

Digital (46, 125, 162)-net over F₉, using

net from sequence [i] based on digital (46, 161)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
  - a curve from the manYPoints database [i]

(125−79, 125, 2057)-Net in Base 9 — Upper bound on s

There is no (46, 125, 2058)-net in base 9, because

1 times m-reduction [i] would yield (46, 124, 2058)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21379 818055 200486 635500 491446 544428 004884 412574 337850 549497 476981 288165 647849 807043 713625 461029 611071 360824 104927 023345 > 9¹²⁴ [i]