MinT - Best Known (150−79, 150, s)-Nets in Base 9

Best Known (150−79, 150, s)-Nets in Base 9

(150−79, 150, 165)-Net over F₉ — Constructive and digital

Digital (71, 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]

(150−79, 150, 222)-Net over F₉ — Digital

Digital (71, 150, 222)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(150−79, 150, 8488)-Net in Base 9 — Upper bound on s

There is no (71, 150, 8489)-net in base 9, because

1 times m-reduction [i] would yield (71, 149, 8489)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15270 712585 012773 670719 221407 266507 902921 176340 495061 165281 901596 356212 338370 737009 241400 099127 931437 970256 767842 441490 810225 728560 278927 098937 > 9¹⁴⁹ [i]