MinT - Best Known (109, 181, s)-Nets in Base 4

Best Known (109, 181, s)-Nets in Base 4

(109, 181, 130)-Net over F₄ — Constructive and digital

Digital (109, 181, 130)-net over F₄, using

t-expansion [i] based on digital (105, 181, 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]

(109, 181, 273)-Net over F₄ — Digital

Digital (109, 181, 273)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(109, 181, 5036)-Net in Base 4 — Upper bound on s

There is no (109, 181, 5037)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 443151 016964 176366 221872 587718 747214 935706 320410 155466 905480 323357 717349 313010 487526 139681 209068 925400 723167 > 4¹⁸¹ [i]