MinT - Best Known (91, 91+134, s)-Nets in Base 4

Best Known (91, 91+134, s)-Nets in Base 4

(91, 91+134, 104)-Net over F₄ — Constructive and digital

Digital (91, 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]

(91, 91+134, 144)-Net over F₄ — Digital

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]

(91, 91+134, 849)-Net in Base 4 — Upper bound on s

There is no (91, 225, 850)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2958 376129 406849 551615 029612 058489 752659 862450 424389 346634 871962 610050 237077 235668 422437 565446 537678 550514 839931 519804 618002 379128 747880 > 4²²⁵ [i]