MinT - Best Known (237−143, 237, s)-Nets in Base 4

Best Known (237−143, 237, s)-Nets in Base 4

(237−143, 237, 104)-Net over F₄ — Constructive and digital

Digital (94, 237, 104)-net over F₄, using

t-expansion [i] based on digital (73, 237, 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]

(237−143, 237, 144)-Net over F₄ — Digital

Digital (94, 237, 144)-net over F₄, using

t-expansion [i] based on digital (91, 237, 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]

(237−143, 237, 854)-Net in Base 4 — Upper bound on s

There is no (94, 237, 855)-net in base 4, because

1 times m-reduction [i] would yield (94, 236, 855)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13026 654679 943632 679301 103313 407562 004597 124608 893419 809215 605317 452714 974794 060162 404316 042466 271571 440144 287755 887008 271432 862609 934412 956636 > 4²³⁶ [i]