MinT - Best Known (240−142, 240, s)-Nets in Base 4

Best Known (240−142, 240, s)-Nets in Base 4

(240−142, 240, 104)-Net over F₄ — Constructive and digital

Digital (98, 240, 104)-net over F₄, using

t-expansion [i] based on digital (73, 240, 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]

(240−142, 240, 144)-Net over F₄ — Digital

Digital (98, 240, 144)-net over F₄, using

t-expansion [i] based on digital (91, 240, 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]

(240−142, 240, 928)-Net in Base 4 — Upper bound on s

There is no (98, 240, 929)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 333794 691048 917289 223130 538210 504879 666079 616972 029585 883375 080939 845408 185529 206979 746633 129062 031794 038444 644406 782642 812383 961266 893088 140224 > 4²⁴⁰ [i]