MinT - Best Known (92, 92+151, s)-Nets in Base 4

Best Known (92, 92+151, s)-Nets in Base 4

(92, 92+151, 104)-Net over F₄ — Constructive and digital

Digital (92, 243, 104)-net over F₄, using

t-expansion [i] based on digital (73, 243, 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]

(92, 92+151, 144)-Net over F₄ — Digital

Digital (92, 243, 144)-net over F₄, using

t-expansion [i] based on digital (91, 243, 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]

(92, 92+151, 779)-Net in Base 4 — Upper bound on s

There is no (92, 243, 780)-net in base 4, because

1 times m-reduction [i] would yield (92, 242, 780)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 52 822524 067595 415723 283774 326740 690263 084681 368743 452012 165900 719867 907704 773650 053424 797413 375546 139439 855030 862592 828103 618463 775927 993628 276108 > 4²⁴² [i]