MinT - Best Known (107, 226, s)-Nets in Base 4

Best Known (107, 226, s)-Nets in Base 4

(107, 226, 130)-Net over F₄ — Constructive and digital

Digital (107, 226, 130)-net over F₄, using

t-expansion [i] based on digital (105, 226, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(107, 226, 144)-Net over F₄ — Digital

Digital (107, 226, 144)-net over F₄, using

t-expansion [i] based on digital (91, 226, 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]

(107, 226, 1455)-Net in Base 4 — Upper bound on s

There is no (107, 226, 1456)-net in base 4, because

1 times m-reduction [i] would yield (107, 225, 1456)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2931 098620 498924 606865 328076 470779 176188 324470 927381 477966 598977 906317 171125 818666 040014 713155 851523 757737 058989 900982 793516 315994 578680 > 4²²⁵ [i]