MinT - Best Known (255−157, 255, s)-Nets in Base 4

Best Known (255−157, 255, s)-Nets in Base 4

(255−157, 255, 104)-Net over F₄ — Constructive and digital

Digital (98, 255, 104)-net over F₄, using

t-expansion [i] based on digital (73, 255, 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]

(255−157, 255, 144)-Net over F₄ — Digital

Digital (98, 255, 144)-net over F₄, using

t-expansion [i] based on digital (91, 255, 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]

(255−157, 255, 846)-Net in Base 4 — Upper bound on s

There is no (98, 255, 847)-net in base 4, because

1 times m-reduction [i] would yield (98, 254, 847)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 911 816507 192724 830761 824676 465725 198671 715205 027318 151397 918762 713162 104771 809327 614757 944154 916039 073904 334104 352723 436485 027726 642530 812884 995457 335421 > 4²⁵⁴ [i]