MinT - Best Known (105, 182, s)-Nets in Base 4

Best Known (105, 182, s)-Nets in Base 4

(105, 182, 130)-Net over F₄ — Constructive and digital

Digital (105, 182, 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]

(105, 182, 225)-Net over F₄ — Digital

Digital (105, 182, 225)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 182, 3662)-Net in Base 4 — Upper bound on s

There is no (105, 182, 3663)-net in base 4, because

1 times m-reduction [i] would yield (105, 181, 3663)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 489975 933719 982448 611715 326308 614554 993485 852114 694872 651294 928934 884955 402400 863137 361969 940711 692656 595210 > 4¹⁸¹ [i]