MinT - Best Known (195−103, 195, s)-Nets in Base 4

Best Known (195−103, 195, s)-Nets in Base 4

(195−103, 195, 104)-Net over F₄ — Constructive and digital

Digital (92, 195, 104)-net over F₄, using

t-expansion [i] based on digital (73, 195, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(195−103, 195, 144)-Net over F₄ — Digital

Digital (92, 195, 144)-net over F₄, using

t-expansion [i] based on digital (91, 195, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(195−103, 195, 1249)-Net in Base 4 — Upper bound on s

There is no (92, 195, 1250)-net in base 4, because

1 times m-reduction [i] would yield (92, 194, 1250)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 642 864132 236815 580327 406614 688072 093411 935739 990538 667347 485073 947994 068275 711848 877439 373331 668021 636913 113105 511776 > 4¹⁹⁴ [i]