MinT - Best Known (100, 100+120, s)-Nets in Base 4

Best Known (100, 100+120, s)-Nets in Base 4

(100, 100+120, 104)-Net over F₄ — Constructive and digital

Digital (100, 220, 104)-net over F₄, using

t-expansion [i] based on digital (73, 220, 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+120, 144)-Net over F₄ — Digital

Digital (100, 220, 144)-net over F₄, using

t-expansion [i] based on digital (91, 220, 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+120, 1197)-Net in Base 4 — Upper bound on s

There is no (100, 220, 1198)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2 845544 261993 754250 698254 197940 413698 883756 252252 256755 724648 234143 610390 793772 656393 153340 524732 440456 065696 366208 588509 536423 938008 > 4²²⁰ [i]