MinT - Best Known (78, 78+67, s)-Nets in Base 4

Best Known (78, 78+67, s)-Nets in Base 4

(78, 78+67, 104)-Net over F₄ — Constructive and digital

Digital (78, 145, 104)-net over F₄, using

t-expansion [i] based on digital (73, 145, 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]

(78, 78+67, 140)-Net over F₄ — Digital

Digital (78, 145, 140)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+67, 1832)-Net in Base 4 — Upper bound on s

There is no (78, 145, 1833)-net in base 4, because

1 times m-reduction [i] would yield (78, 144, 1833)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 500 140119 404709 462053 570002 148638 640737 029573 919792 589978 200799 215018 983029 704125 299020 > 4¹⁴⁴ [i]