MinT - Best Known (247−151, 247, s)-Nets in Base 4

Best Known (247−151, 247, s)-Nets in Base 4

(247−151, 247, 104)-Net over F₄ — Constructive and digital

Digital (96, 247, 104)-net over F₄, using

t-expansion [i] based on digital (73, 247, 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]

(247−151, 247, 144)-Net over F₄ — Digital

Digital (96, 247, 144)-net over F₄, using

t-expansion [i] based on digital (91, 247, 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]

(247−151, 247, 843)-Net in Base 4 — Upper bound on s

There is no (96, 247, 844)-net in base 4, because

1 times m-reduction [i] would yield (96, 246, 844)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13115 079730 282355 500895 360954 509407 698846 760232 173047 319729 322406 969829 261808 878259 694583 124979 169730 854875 338704 799813 899210 103929 820691 051691 416587 > 4²⁴⁶ [i]