MinT - Best Known (211−120, 211, s)-Nets in Base 4

Best Known (211−120, 211, s)-Nets in Base 4

(211−120, 211, 104)-Net over F₄ — Constructive and digital

Digital (91, 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]

(211−120, 211, 144)-Net over F₄ — Digital

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]

(211−120, 211, 964)-Net in Base 4 — Upper bound on s

There is no (91, 211, 965)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 457344 609264 983454 971479 038993 174265 876872 475287 749781 409792 623088 667452 342442 910514 001581 639612 302560 286898 216231 676596 112120 > 4²¹¹ [i]