MinT - Best Known (147−76, 147, s)-Nets in Base 9

Best Known (147−76, 147, s)-Nets in Base 9

(147−76, 147, 165)-Net over F₉ — Constructive and digital

Digital (71, 147, 165)-net over F₉, using

t-expansion [i] based on digital (64, 147, 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]

(147−76, 147, 236)-Net over F₉ — Digital

Digital (71, 147, 236)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−76, 147, 9205)-Net in Base 9 — Upper bound on s

There is no (71, 147, 9206)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 188 448138 858638 275754 250351 379828 761623 841168 288542 549837 320874 285641 277851 513593 555426 736825 989973 831128 405088 619069 219347 295385 749862 758625 > 9¹⁴⁷ [i]