MinT - Best Known (146−73, 146, s)-Nets in Base 4

Best Known (146−73, 146, s)-Nets in Base 4

(146−73, 146, 104)-Net over F₄ — Constructive and digital

Digital (73, 146, 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]

(146−73, 146, 112)-Net over F₄ — Digital

Digital (73, 146, 112)-net over F₄, using

net from sequence [i] based on digital (73, 111)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 112, using
  - Drinfeld modules of rank 1 [i]

(146−73, 146, 1237)-Net in Base 4 — Upper bound on s

There is no (73, 146, 1238)-net in base 4, because

1 times m-reduction [i] would yield (73, 145, 1238)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2035 849281 893197 459144 025903 530227 585012 174028 508543 234763 937901 105420 015821 732101 154870 > 4¹⁴⁵ [i]