MinT - Best Known (211−114, 211, s)-Nets in Base 4

Best Known (211−114, 211, s)-Nets in Base 4

(211−114, 211, 104)-Net over F₄ — Constructive and digital

Digital (97, 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]

(211−114, 211, 144)-Net over F₄ — Digital

Digital (97, 211, 144)-net over F₄, using

t-expansion [i] based on digital (91, 211, 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]

(211−114, 211, 1199)-Net in Base 4 — Upper bound on s

There is no (97, 211, 1200)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 948782 830991 856812 823453 536449 510820 407134 445915 762806 288608 796251 119974 501763 159097 938541 676659 780565 958114 787677 946701 520808 > 4²¹¹ [i]