MinT - Best Known (209−108, 209, s)-Nets in Base 4

Best Known (209−108, 209, s)-Nets in Base 4

(209−108, 209, 104)-Net over F₄ — Constructive and digital

Digital (101, 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]

(209−108, 209, 144)-Net over F₄ — Digital

Digital (101, 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]

(209−108, 209, 1450)-Net in Base 4 — Upper bound on s

There is no (101, 209, 1451)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 679008 216138 146399 498662 755295 534315 051978 649174 314417 068860 327342 843549 929150 506129 151371 107763 501169 321136 070165 515182 621360 > 4²⁰⁹ [i]