MinT - Best Known (75, 211, s)-Nets in Base 4

Best Known (75, 211, s)-Nets in Base 4

(75, 211, 104)-Net over F₄ — Constructive and digital

Digital (75, 211, 104)-net over F₄, using

t-expansion [i] based on digital (73, 211, 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]

(75, 211, 112)-Net over F₄ — Digital

Digital (75, 211, 112)-net over F₄, using

t-expansion [i] based on digital (73, 211, 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]

(75, 211, 589)-Net in Base 4 — Upper bound on s

There is no (75, 211, 590)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 787037 426290 355320 455839 094306 154279 015512 064043 587511 395134 596825 663388 428863 722514 534422 494832 673095 803940 255951 216647 462795 > 4²¹¹ [i]