MinT - Best Known (98, 98+152, s)-Nets in Base 4

Best Known (98, 98+152, s)-Nets in Base 4

(98, 98+152, 104)-Net over F₄ — Constructive and digital

Digital (98, 250, 104)-net over F₄, using

t-expansion [i] based on digital (73, 250, 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]

(98, 98+152, 144)-Net over F₄ — Digital

Digital (98, 250, 144)-net over F₄, using

t-expansion [i] based on digital (91, 250, 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]

(98, 98+152, 866)-Net in Base 4 — Upper bound on s

There is no (98, 250, 867)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 379921 724362 628397 202487 293486 721905 100140 019849 182246 645933 151379 135798 039950 951334 467675 258888 593643 828587 489714 968298 255337 478104 714589 157576 724392 > 4²⁵⁰ [i]