MinT - Best Known (242−145, 242, s)-Nets in Base 4

Best Known (242−145, 242, s)-Nets in Base 4

(242−145, 242, 104)-Net over F₄ — Constructive and digital

Digital (97, 242, 104)-net over F₄, using

t-expansion [i] based on digital (73, 242, 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]

(242−145, 242, 144)-Net over F₄ — Digital

Digital (97, 242, 144)-net over F₄, using

t-expansion [i] based on digital (91, 242, 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]

(242−145, 242, 895)-Net in Base 4 — Upper bound on s

There is no (97, 242, 896)-net in base 4, because

1 times m-reduction [i] would yield (97, 241, 896)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 12 515257 628918 383422 831805 609018 205013 162331 717967 073891 830510 408682 189648 692752 764200 284785 309001 422652 477992 704404 666507 571322 855390 694129 540111 > 4²⁴¹ [i]