MinT - Best Known (92, 92+161, s)-Nets in Base 4

Best Known (92, 92+161, s)-Nets in Base 4

(92, 92+161, 104)-Net over F₄ — Constructive and digital

Digital (92, 253, 104)-net over F₄, using

t-expansion [i] based on digital (73, 253, 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+161, 144)-Net over F₄ — Digital

Digital (92, 253, 144)-net over F₄, using

t-expansion [i] based on digital (91, 253, 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+161, 739)-Net in Base 4 — Upper bound on s

There is no (92, 253, 740)-net in base 4, because

1 times m-reduction [i] would yield (92, 252, 740)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 55 342272 523403 147866 761097 943558 857959 882382 247421 478617 485103 872548 565546 499886 611833 350815 098948 326521 468593 143406 870257 939674 854865 406497 393198 310630 > 4²⁵² [i]