MinT - Best Known (209−106, 209, s)-Nets in Base 4

Best Known (209−106, 209, s)-Nets in Base 4

(209−106, 209, 104)-Net over F₄ — Constructive and digital

Digital (103, 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]

(209−106, 209, 144)-Net over F₄ — Digital

Digital (103, 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]

(209−106, 209, 1581)-Net in Base 4 — Upper bound on s

There is no (103, 209, 1582)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 683764 784406 536069 824269 034914 652971 152488 804054 446311 158323 373229 913185 531824 014236 776377 711335 486737 102554 851895 951427 770400 > 4²⁰⁹ [i]