MinT - Best Known (209−112, 209, s)-Nets in Base 4

Best Known (209−112, 209, s)-Nets in Base 4

(209−112, 209, 104)-Net over F₄ — Constructive and digital

Digital (97, 209, 104)-net over F₄, using

t-expansion [i] based on digital (73, 209, 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]

(209−112, 209, 144)-Net over F₄ — Digital

Digital (97, 209, 144)-net over F₄, using

t-expansion [i] based on digital (91, 209, 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]

(209−112, 209, 1232)-Net in Base 4 — Upper bound on s

There is no (97, 209, 1233)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 696543 612465 343969 461192 438513 622526 395532 021921 370687 182645 070456 334359 137807 129655 121791 099377 842759 725468 421017 463119 744280 > 4²⁰⁹ [i]