MinT - Best Known (248−151, 248, s)-Nets in Base 4

Best Known (248−151, 248, s)-Nets in Base 4

(248−151, 248, 104)-Net over F₄ — Constructive and digital

Digital (97, 248, 104)-net over F₄, using

t-expansion [i] based on digital (73, 248, 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]

(248−151, 248, 144)-Net over F₄ — Digital

Digital (97, 248, 144)-net over F₄, using

t-expansion [i] based on digital (91, 248, 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]

(248−151, 248, 860)-Net in Base 4 — Upper bound on s

There is no (97, 248, 861)-net in base 4, because

1 times m-reduction [i] would yield (97, 247, 861)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 53126 346473 321461 400348 851861 851483 417415 470299 184355 567903 140295 879727 825139 050316 113185 785347 306596 345118 414002 237812 855814 705748 899046 656804 278196 > 4²⁴⁷ [i]