MinT - Best Known (182−73, 182, s)-Nets in Base 4

Best Known (182−73, 182, s)-Nets in Base 4

(182−73, 182, 130)-Net over F₄ — Constructive and digital

Digital (109, 182, 130)-net over F₄, using

t-expansion [i] based on 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]

(182−73, 182, 267)-Net over F₄ — Digital

Digital (109, 182, 267)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−73, 182, 5036)-Net in Base 4 — Upper bound on s

There is no (109, 182, 5037)-net in base 4, because

1 times m-reduction [i] would yield (109, 181, 5037)-net in base 4, but
- 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]