MinT - Best Known (39, 127, s)-Nets in Base 9

Best Known (39, 127, s)-Nets in Base 9

(39, 127, 81)-Net over F₉ — Constructive and digital

Digital (39, 127, 81)-net over F₉, using

t-expansion [i] based on digital (32, 127, 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]

(39, 127, 140)-Net over F₉ — Digital

Digital (39, 127, 140)-net over F₉, using

net from sequence [i] based on digital (39, 139)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
  - a curve from the manYPoints database [i]

(39, 127, 1198)-Net in Base 9 — Upper bound on s

There is no (39, 127, 1199)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 931168 063840 865279 753066 511568 154373 296932 316359 385392 762380 459301 681541 575782 743525 642582 168567 114259 856730 149604 353185 > 9¹²⁷ [i]