MinT - Best Known (256−153, 256, s)-Nets in Base 4

Best Known (256−153, 256, s)-Nets in Base 4

(256−153, 256, 104)-Net over F₄ — Constructive and digital

Digital (103, 256, 104)-net over F₄, using

t-expansion [i] based on digital (73, 256, 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]

(256−153, 256, 144)-Net over F₄ — Digital

Digital (103, 256, 144)-net over F₄, using

t-expansion [i] based on digital (91, 256, 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]

(256−153, 256, 955)-Net in Base 4 — Upper bound on s

There is no (103, 256, 956)-net in base 4, because

1 times m-reduction [i] would yield (103, 255, 956)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3590 370601 866563 867393 401676 198344 003242 117661 797839 692312 091942 232375 730059 413186 782027 963173 488747 355307 231171 229842 113387 682928 392916 286401 573622 127048 > 4²⁵⁵ [i]