MinT - Best Known (199−119, 199, s)-Nets in Base 4

Best Known (199−119, 199, s)-Nets in Base 4

(199−119, 199, 104)-Net over F₄ — Constructive and digital

Digital (80, 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]

(199−119, 199, 112)-Net over F₄ — Digital

Digital (80, 199, 112)-net over F₄, using

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

(199−119, 199, 749)-Net in Base 4 — Upper bound on s

There is no (80, 199, 750)-net in base 4, because

1 times m-reduction [i] would yield (80, 198, 750)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 163079 574977 673647 442267 262645 389744 421348 045167 733896 264967 540374 939603 056846 192033 001462 758979 798901 740884 120044 237816 > 4¹⁹⁸ [i]