MinT - Best Known (230−125, 230, s)-Nets in Base 4

Best Known (230−125, 230, s)-Nets in Base 4

(230−125, 230, 130)-Net over F₄ — Constructive and digital

Digital (105, 230, 130)-net over F₄, using

net from sequence [i] based on digital (105, 129)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
  - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(230−125, 230, 144)-Net over F₄ — Digital

Digital (105, 230, 144)-net over F₄, using

t-expansion [i] based on digital (91, 230, 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]

(230−125, 230, 1284)-Net in Base 4 — Upper bound on s

There is no (105, 230, 1285)-net in base 4, because

1 times m-reduction [i] would yield (105, 229, 1285)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 745046 180113 456747 918670 177088 300310 797254 841976 759583 667660 710751 426993 926074 954425 471934 354443 026851 829646 370734 905240 120170 252617 566080 > 4²²⁹ [i]