MinT - Best Known (225−133, 225, s)-Nets in Base 4

Best Known (225−133, 225, s)-Nets in Base 4

(225−133, 225, 104)-Net over F₄ — Constructive and digital

Digital (92, 225, 104)-net over F₄, using

t-expansion [i] based on digital (73, 225, 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]

(225−133, 225, 144)-Net over F₄ — Digital

Digital (92, 225, 144)-net over F₄, using

t-expansion [i] based on digital (91, 225, 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]

(225−133, 225, 882)-Net in Base 4 — Upper bound on s

There is no (92, 225, 883)-net in base 4, because

1 times m-reduction [i] would yield (92, 224, 883)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 738 371508 073488 103192 453904 061522 364102 151201 485629 855917 779026 204853 765889 717128 460340 578298 503751 957415 302025 562796 343422 623784 123175 > 4²²⁴ [i]