MinT - Best Known (142−69, 142, s)-Nets in Base 4

Best Known (142−69, 142, s)-Nets in Base 4

(142−69, 142, 104)-Net over F₄ — Constructive and digital

Digital (73, 142, 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]

(142−69, 142, 117)-Net over F₄ — Digital

Digital (73, 142, 117)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−69, 142, 1388)-Net in Base 4 — Upper bound on s

There is no (73, 142, 1389)-net in base 4, because

1 times m-reduction [i] would yield (73, 141, 1389)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 845672 790115 119655 415917 632641 104868 354964 674186 129814 710352 122503 679491 258889 173350 > 4¹⁴¹ [i]