MinT - Best Known (150−77, 150, s)-Nets in Base 9

Best Known (150−77, 150, s)-Nets in Base 9

(150−77, 150, 165)-Net over F₉ — Constructive and digital

Digital (73, 150, 165)-net over F₉, using

t-expansion [i] based on digital (64, 150, 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]

(150−77, 150, 247)-Net over F₉ — Digital

Digital (73, 150, 247)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−77, 150, 10336)-Net in Base 9 — Upper bound on s

There is no (73, 150, 10337)-net in base 9, because

1 times m-reduction [i] would yield (73, 149, 10337)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15238 546934 967885 039972 434673 687155 009503 726061 179337 170051 768466 380191 916596 290973 314061 478452 143960 849051 427992 564488 108462 881244 107998 844657 > 9¹⁴⁹ [i]