MinT - Best Known (236−133, 236, s)-Nets in Base 4

Best Known (236−133, 236, s)-Nets in Base 4

(236−133, 236, 104)-Net over F₄ — Constructive and digital

Digital (103, 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]

(236−133, 236, 144)-Net over F₄ — Digital

Digital (103, 236, 144)-net over F₄, using

t-expansion [i] based on digital (91, 236, 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]

(236−133, 236, 1125)-Net in Base 4 — Upper bound on s

There is no (103, 236, 1126)-net in base 4, because

1 times m-reduction [i] would yield (103, 235, 1126)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3073 846389 434757 025618 080590 631084 857326 432523 093843 782908 414721 340293 832045 722542 328341 630753 303223 899579 101517 353861 398223 680929 554723 951086 > 4²³⁵ [i]