MinT - Best Known (92, 92+125, s)-Nets in Base 4

Best Known (92, 92+125, s)-Nets in Base 4

(92, 92+125, 104)-Net over F₄ — Constructive and digital

Digital (92, 217, 104)-net over F₄, using

t-expansion [i] based on digital (73, 217, 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]

(92, 92+125, 144)-Net over F₄ — Digital

Digital (92, 217, 144)-net over F₄, using

t-expansion [i] based on digital (91, 217, 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]

(92, 92+125, 948)-Net in Base 4 — Upper bound on s

There is no (92, 217, 949)-net in base 4, because

1 times m-reduction [i] would yield (92, 216, 949)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11530 739186 284322 527302 934527 919615 721650 489821 552334 859247 041315 872906 908984 413269 800524 379879 315366 008316 202412 402651 902197 469120 > 4²¹⁶ [i]