MinT - Best Known (174−96, 174, s)-Nets in Base 4

Best Known (174−96, 174, s)-Nets in Base 4

(174−96, 174, 104)-Net over F₄ — Constructive and digital

Digital (78, 174, 104)-net over F₄, using

t-expansion [i] based on digital (73, 174, 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]

(174−96, 174, 112)-Net over F₄ — Digital

Digital (78, 174, 112)-net over F₄, using

t-expansion [i] based on digital (73, 174, 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]

(174−96, 174, 912)-Net in Base 4 — Upper bound on s

There is no (78, 174, 913)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 602 547305 385539 892697 742878 571136 867624 996883 026593 219909 525657 317033 957501 811542 798111 559020 402225 848220 > 4¹⁷⁴ [i]