MinT - Best Known (114−79, 114, s)-Nets in Base 9

Best Known (114−79, 114, s)-Nets in Base 9

(114−79, 114, 81)-Net over F₉ — Constructive and digital

Digital (35, 114, 81)-net over F₉, using

t-expansion [i] based on digital (32, 114, 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]

(114−79, 114, 128)-Net over F₉ — Digital

Digital (35, 114, 128)-net over F₉, using

t-expansion [i] based on digital (33, 114, 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]

(114−79, 114, 1096)-Net in Base 9 — Upper bound on s

There is no (35, 114, 1097)-net in base 9, because

1 times m-reduction [i] would yield (35, 113, 1097)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 694087 851719 610120 882099 763912 964090 390117 369031 461288 466117 896732 518763 426554 858780 037100 825338 777190 895417 > 9¹¹³ [i]