MinT - Best Known (71, 71+110, s)-Nets in Base 4

Best Known (71, 71+110, s)-Nets in Base 4

(71, 71+110, 66)-Net over F₄ — Constructive and digital

Digital (71, 181, 66)-net over F₄, using

t-expansion [i] based on digital (49, 181, 66)-net over F₄, using
- net from sequence [i] based on digital (49, 65)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 49 and N(F) ≥ 66, using
    - T₆ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(71, 71+110, 105)-Net over F₄ — Digital

Digital (71, 181, 105)-net over F₄, using

t-expansion [i] based on digital (70, 181, 105)-net over F₄, using
- net from sequence [i] based on digital (70, 104)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 70 and N(F) ≥ 105, using
    - Drinfeld modules of rank 1 [i]

(71, 71+110, 637)-Net in Base 4 — Upper bound on s

There is no (71, 181, 638)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 089036 906214 133711 173124 515707 092005 634525 910437 446462 522171 635965 439854 040277 223611 271665 111350 794062 177660 > 4¹⁸¹ [i]