MinT - Best Known (199−118, 199, s)-Nets in Base 4

Best Known (199−118, 199, s)-Nets in Base 4

(199−118, 199, 104)-Net over F₄ — Constructive and digital

Digital (81, 199, 104)-net over F₄, using

t-expansion [i] based on digital (73, 199, 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]

(199−118, 199, 129)-Net over F₄ — Digital

Digital (81, 199, 129)-net over F₄, using

net from sequence [i] based on digital (81, 128)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
  - Drinfeld modules of rank 1 [i]

(199−118, 199, 768)-Net in Base 4 — Upper bound on s

There is no (81, 199, 769)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 655289 646045 804467 592205 119304 414338 508639 615909 675457 634432 874904 373657 792087 450579 267918 136561 103504 842244 849061 329152 > 4¹⁹⁹ [i]