MinT - Best Known (100, 100+122, s)-Nets in Base 4

Best Known (100, 100+122, s)-Nets in Base 4

(100, 100+122, 104)-Net over F₄ — Constructive and digital

Digital (100, 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]

(100, 100+122, 144)-Net over F₄ — Digital

Digital (100, 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]

(100, 100+122, 1170)-Net in Base 4 — Upper bound on s

There is no (100, 222, 1171)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 47 746117 061059 233076 711372 338007 439326 593483 595178 700826 358495 587324 952266 696709 651487 103346 844819 394825 607164 408257 085987 376440 801600 > 4²²² [i]