MinT - Best Known (245−148, 245, s)-Nets in Base 4

Best Known (245−148, 245, s)-Nets in Base 4

(245−148, 245, 104)-Net over F₄ — Constructive and digital

Digital (97, 245, 104)-net over F₄, using

t-expansion [i] based on digital (73, 245, 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]

(245−148, 245, 144)-Net over F₄ — Digital

Digital (97, 245, 144)-net over F₄, using

t-expansion [i] based on digital (91, 245, 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]

(245−148, 245, 871)-Net in Base 4 — Upper bound on s

There is no (97, 245, 872)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3260 989094 289187 452468 265795 365145 685530 305877 700746 790403 203377 129031 255961 387194 201416 787063 851016 053448 662135 170547 186659 828992 809776 781451 669884 > 4²⁴⁵ [i]