MinT - Best Known (222−124, 222, s)-Nets in Base 4

Best Known (222−124, 222, s)-Nets in Base 4

(222−124, 222, 104)-Net over F₄ — Constructive and digital

Digital (98, 222, 104)-net over F₄, using

t-expansion [i] based on digital (73, 222, 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]

(222−124, 222, 144)-Net over F₄ — Digital

Digital (98, 222, 144)-net over F₄, using

t-expansion [i] based on digital (91, 222, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(222−124, 222, 1091)-Net in Base 4 — Upper bound on s

There is no (98, 222, 1092)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 46 372397 380035 944050 171961 973028 004060 834806 484778 123743 378622 570165 351003 787074 000775 748608 178360 890168 022907 877014 191077 878212 254000 > 4²²² [i]