MinT - Best Known (237−145, 237, s)-Nets in Base 4

Best Known (237−145, 237, s)-Nets in Base 4

(237−145, 237, 104)-Net over F₄ — Constructive and digital

Digital (92, 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]

(237−145, 237, 144)-Net over F₄ — Digital

Digital (92, 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]

(237−145, 237, 808)-Net in Base 4 — Upper bound on s

There is no (92, 237, 809)-net in base 4, because

1 times m-reduction [i] would yield (92, 236, 809)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12675 273538 952443 333633 399847 185317 419995 977709 108726 671343 697465 012086 605645 183749 940333 010964 789661 841799 771651 217132 409573 865055 129909 915340 > 4²³⁶ [i]