MinT - Best Known (209−118, 209, s)-Nets in Base 4

Best Known (209−118, 209, s)-Nets in Base 4

(209−118, 209, 104)-Net over F₄ — Constructive and digital

Digital (91, 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]

(209−118, 209, 144)-Net over F₄ — Digital

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]

(209−118, 209, 984)-Net in Base 4 — Upper bound on s

There is no (91, 209, 985)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 684503 109047 871870 238284 699973 920338 739737 696000 381470 026716 093826 446276 590569 282432 441954 146444 671428 509793 881985 704956 514752 > 4²⁰⁹ [i]