MinT - Best Known (248−157, 248, s)-Nets in Base 4

Best Known (248−157, 248, s)-Nets in Base 4

(248−157, 248, 104)-Net over F₄ — Constructive and digital

Digital (91, 248, 104)-net over F₄, using

t-expansion [i] based on digital (73, 248, 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]

(248−157, 248, 144)-Net over F₄ — Digital

Digital (91, 248, 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]

(248−157, 248, 739)-Net in Base 4 — Upper bound on s

There is no (91, 248, 740)-net in base 4, because

1 times m-reduction [i] would yield (91, 247, 740)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 51580 666374 604699 489557 996650 200845 602924 476388 271646 227324 112661 948095 288146 630753 967303 585378 209750 704899 932347 015358 778121 112504 227354 713934 548936 > 4²⁴⁷ [i]