MinT - Best Known (191−116, 191, s)-Nets in Base 4

Best Known (191−116, 191, s)-Nets in Base 4

(191−116, 191, 104)-Net over F₄ — Constructive and digital

Digital (75, 191, 104)-net over F₄, using

t-expansion [i] based on digital (73, 191, 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]

(191−116, 191, 112)-Net over F₄ — Digital

Digital (75, 191, 112)-net over F₄, using

t-expansion [i] based on digital (73, 191, 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]

(191−116, 191, 672)-Net in Base 4 — Upper bound on s

There is no (75, 191, 673)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 356731 901319 969982 098583 293476 140394 296505 611891 666126 315693 246420 784367 452863 542210 970868 509806 107278 259908 564800 > 4¹⁹¹ [i]