MinT - Best Known (150−83, 150, s)-Nets in Base 9

Best Known (150−83, 150, s)-Nets in Base 9

(150−83, 150, 165)-Net over F₉ — Constructive and digital

Digital (67, 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]

(150−83, 150, 192)-Net over F₉ — Digital

Digital (67, 150, 192)-net over F₉, using

t-expansion [i] based on digital (61, 150, 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]

(150−83, 150, 5899)-Net in Base 9 — Upper bound on s

There is no (67, 150, 5900)-net in base 9, because

1 times m-reduction [i] would yield (67, 149, 5900)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15232 279681 682571 407760 827510 732487 706978 050563 771403 823841 365810 169648 098332 802941 717155 939206 480816 478335 128155 922149 728561 558316 404353 842529 > 9¹⁴⁹ [i]