MinT - Best Known (73, 73+130, s)-Nets in Base 4

Best Known (73, 73+130, s)-Nets in Base 4

(73, 73+130, 104)-Net over F₄ — Constructive and digital

Digital (73, 203, 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+130, 112)-Net over F₄ — Digital

Digital (73, 203, 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+130, 581)-Net in Base 4 — Upper bound on s

There is no (73, 203, 582)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 170 842295 150324 690130 019148 148435 464361 385928 350906 053500 727844 585907 257474 919232 096783 648768 480662 047499 882169 697312 485355 > 4²⁰³ [i]