MinT - Best Known (73, 174, s)-Nets in Base 4

Best Known (73, 174, s)-Nets in Base 4

(73, 174, 104)-Net over F₄ — Constructive and digital

Digital (73, 174, 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, 174, 112)-Net over F₄ — Digital

Digital (73, 174, 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, 174, 746)-Net in Base 4 — Upper bound on s

There is no (73, 174, 747)-net in base 4, because

1 times m-reduction [i] would yield (73, 173, 747)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 151 984793 235842 558842 324059 258745 994381 532948 508800 721752 578063 313091 274381 963032 524348 605628 550300 179916 > 4¹⁷³ [i]