MinT - Best Known (127−90, 127, s)-Nets in Base 9

Best Known (127−90, 127, s)-Nets in Base 9

(127−90, 127, 81)-Net over F₉ — Constructive and digital

Digital (37, 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]

(127−90, 127, 128)-Net over F₉ — Digital

Digital (37, 127, 128)-net over F₉, using

t-expansion [i] based on digital (33, 127, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(127−90, 127, 1059)-Net in Base 9 — Upper bound on s

There is no (37, 127, 1060)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 817703 880547 384395 916267 452165 105733 518275 116865 852449 858991 798435 144669 497633 839028 184483 462440 196003 536664 874661 475745 > 9¹²⁷ [i]