MinT - Best Known (73, 73+124, s)-Nets in Base 4

Best Known (73, 73+124, s)-Nets in Base 4

(73, 73+124, 104)-Net over F₄ — Constructive and digital

Digital (73, 197, 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+124, 112)-Net over F₄ — Digital

Digital (73, 197, 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+124, 603)-Net in Base 4 — Upper bound on s

There is no (73, 197, 604)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 43347 642679 597448 747251 683886 278691 764608 689315 164588 872354 004581 865267 781070 325653 147359 387273 821377 832857 125417 463440 > 4¹⁹⁷ [i]