MinT - Best Known (73, 73+173, s)-Nets in Base 4

Best Known (73, 73+173, s)-Nets in Base 4

(73, 73+173, 104)-Net over F₄ — Constructive and digital

Digital (73, 246, 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]

(73, 73+173, 112)-Net over F₄ — Digital

Digital (73, 246, 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]

(73, 73+173, 499)-Net in Base 4 — Upper bound on s

There is no (73, 246, 500)-net in base 4, because

1 times m-reduction [i] would yield (73, 245, 500)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 3314 170028 174018 552440 186729 119089 818629 596846 008167 423672 326130 348032 315967 754939 919882 834109 451690 210209 266392 486685 031499 717505 794909 437623 601256 > 4²⁴⁵ [i]