MinT - Best Known (91, 91+125, s)-Nets in Base 4

Best Known (91, 91+125, s)-Nets in Base 4

(91, 91+125, 104)-Net over F₄ — Constructive and digital

Digital (91, 216, 104)-net over F₄, using

t-expansion [i] based on digital (73, 216, 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+125, 144)-Net over F₄ — Digital

Digital (91, 216, 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+125, 926)-Net in Base 4 — Upper bound on s

There is no (91, 216, 927)-net in base 4, because

1 times m-reduction [i] would yield (91, 215, 927)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2895 925032 305886 196553 800649 055881 355725 825159 641365 117821 558470 240586 880306 312760 451801 646043 004551 283152 817511 685710 969407 615980 > 4²¹⁵ [i]