MinT - Best Known (46, 46+77, s)-Nets in Base 9

Best Known (46, 46+77, s)-Nets in Base 9

(46, 46+77, 81)-Net over F₉ — Constructive and digital

Digital (46, 123, 81)-net over F₉, using

t-expansion [i] based on digital (32, 123, 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]

(46, 46+77, 162)-Net over F₉ — Digital

Digital (46, 123, 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]

(46, 46+77, 2151)-Net in Base 9 — Upper bound on s

There is no (46, 123, 2152)-net in base 9, because

1 times m-reduction [i] would yield (46, 122, 2152)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 265 274557 657489 130624 915182 054080 987863 641291 561354 878697 603804 523391 883126 160714 610966 023317 426503 441714 266715 981441 > 9¹²² [i]