MinT - Best Known (144−76, 144, s)-Nets in Base 9

Best Known (144−76, 144, s)-Nets in Base 9

(144−76, 144, 165)-Net over F₉ — Constructive and digital

Digital (68, 144, 165)-net over F₉, using

t-expansion [i] based on digital (64, 144, 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]

(144−76, 144, 213)-Net over F₉ — Digital

Digital (68, 144, 213)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−76, 144, 7735)-Net in Base 9 — Upper bound on s

There is no (68, 144, 7736)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 258229 476193 892666 080336 599867 637484 888437 233434 149963 321658 946993 849212 749390 555547 472218 615399 885699 006922 027179 051323 953048 114500 383617 > 9¹⁴⁴ [i]