MinT - Best Known (251−115, 251, s)-Nets in Base 4

Best Known (251−115, 251, s)-Nets in Base 4

(251−115, 251, 130)-Net over F₄ — Constructive and digital

Digital (136, 251, 130)-net over F₄, using

t-expansion [i] based on digital (105, 251, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(251−115, 251, 232)-Net over F₄ — Digital

Digital (136, 251, 232)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(251−115, 251, 3170)-Net in Base 4 — Upper bound on s

There is no (136, 251, 3171)-net in base 4, because

1 times m-reduction [i] would yield (136, 250, 3171)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3 300415 811007 079500 151342 126990 106254 889637 923673 278784 435692 365105 881182 961977 676971 152347 423162 828560 829260 752762 569492 870588 726072 223873 619308 909840 > 4²⁵⁰ [i]