MinT - Best Known (231−158, 231, s)-Nets in Base 4

Best Known (231−158, 231, s)-Nets in Base 4

(231−158, 231, 104)-Net over F₄ — Constructive and digital

Digital (73, 231, 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]

(231−158, 231, 112)-Net over F₄ — Digital

Digital (73, 231, 112)-net over F₄, using

net from sequence [i] based on digital (73, 111)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
  - Drinfeld modules of rank 1 [i]

(231−158, 231, 517)-Net in Base 4 — Upper bound on s

There is no (73, 231, 518)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 365447 282048 935275 420072 982835 494006 698759 066571 488470 228151 717818 571850 127401 642803 174561 473740 643989 749711 910232 842382 804689 561756 451584 > 4²³¹ [i]