MinT - Best Known (191−133, 191, s)-Nets in Base 4

Best Known (191−133, 191, s)-Nets in Base 4

(191−133, 191, 66)-Net over F₄ — Constructive and digital

Digital (58, 191, 66)-net over F₄, using

t-expansion [i] based on digital (49, 191, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(191−133, 191, 91)-Net over F₄ — Digital

Digital (58, 191, 91)-net over F₄, using

t-expansion [i] based on digital (50, 191, 91)-net over F₄, using
- net from sequence [i] based on digital (50, 90)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 50 and N(F) ≥ 91, using
    - a curve from the manYPoints database [i]

(191−133, 191, 406)-Net in Base 4 — Upper bound on s

There is no (58, 191, 407)-net in base 4, because

1 times m-reduction [i] would yield (58, 190, 407)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 783390 216863 812850 632840 640592 647868 780185 073855 561220 425384 656873 095563 138292 987708 929669 292093 709033 791649 972390 > 4¹⁹⁰ [i]