MinT - Best Known (140−76, 140, s)-Nets in Base 9

Best Known (140−76, 140, s)-Nets in Base 9

(140−76, 140, 165)-Net over F₉ — Constructive and digital

Digital (64, 140, 165)-net over F₉, using

net from sequence [i] based on digital (64, 164)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 64 and N(F) ≥ 165, using
  - T₄ from the second tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(140−76, 140, 192)-Net over F₉ — Digital

Digital (64, 140, 192)-net over F₉, using

t-expansion [i] based on digital (61, 140, 192)-net over F₉, using
- net from sequence [i] based on digital (61, 191)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 61 and N(F) ≥ 192, using
    - Drinfeld modules of rank 1 [i]

(140−76, 140, 6133)-Net in Base 9 — Upper bound on s

There is no (64, 140, 6134)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 402869 897457 406770 658881 946465 418888 891343 653505 911592 613479 337632 489113 977541 046183 373384 213479 945655 129161 736445 157780 460448 348385 > 9¹⁴⁰ [i]