MinT - Best Known (172−84, 172, s)-Nets in Base 4

Best Known (172−84, 172, s)-Nets in Base 4

(172−84, 172, 104)-Net over F₄ — Constructive and digital

Digital (88, 172, 104)-net over F₄, using

t-expansion [i] based on digital (73, 172, 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]

(172−84, 172, 136)-Net over F₄ — Digital

Digital (88, 172, 136)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(172−84, 172, 1573)-Net in Base 4 — Upper bound on s

There is no (88, 172, 1574)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 36 134264 981859 302055 087235 526659 839068 060300 247370 944798 232318 768067 827571 777908 466210 721843 329132 137600 > 4¹⁷² [i]