MinT - Best Known (236−158, 236, s)-Nets in Base 4

Best Known (236−158, 236, s)-Nets in Base 4

(236−158, 236, 104)-Net over F₄ — Constructive and digital

Digital (78, 236, 104)-net over F₄, using

t-expansion [i] based on digital (73, 236, 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]

(236−158, 236, 112)-Net over F₄ — Digital

Digital (78, 236, 112)-net over F₄, using

t-expansion [i] based on digital (73, 236, 112)-net over F₄, using
- net from sequence [i] based on digital (73, 111)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
    - Drinfeld modules of rank 1 [i]

(236−158, 236, 570)-Net in Base 4 — Upper bound on s

There is no (78, 236, 571)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12599 337409 030185 804791 522627 629180 618873 468861 018624 447016 883164 623461 391150 548523 336848 099042 401619 854137 314575 825675 884318 500784 391120 707840 > 4²³⁶ [i]