MinT - Best Known (185−112, 185, s)-Nets in Base 4

Best Known (185−112, 185, s)-Nets in Base 4

(185−112, 185, 104)-Net over F₄ — Constructive and digital

Digital (73, 185, 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]

(185−112, 185, 112)-Net over F₄ — Digital

Digital (73, 185, 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]

(185−112, 185, 660)-Net in Base 4 — Upper bound on s

There is no (73, 185, 661)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2521 986221 996400 475541 651277 386543 836458 176305 724416 293123 821561 718496 799981 536294 659515 527642 458489 307738 755280 > 4¹⁸⁵ [i]