MinT - Best Known (169−81, 169, s)-Nets in Base 4

Best Known (169−81, 169, s)-Nets in Base 4

(169−81, 169, 104)-Net over F₄ — Constructive and digital

Digital (88, 169, 104)-net over F₄, using

t-expansion [i] based on digital (73, 169, 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]

(169−81, 169, 142)-Net over F₄ — Digital

Digital (88, 169, 142)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(169−81, 169, 1742)-Net in Base 4 — Upper bound on s

There is no (88, 169, 1743)-net in base 4, because

1 times m-reduction [i] would yield (88, 168, 1743)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 140293 803523 132635 772285 176282 144352 701759 810919 836385 024509 955705 100595 466005 269112 475319 488687 245022 > 4¹⁶⁸ [i]