MinT - Best Known (219−110, 219, s)-Nets in Base 4

Best Known (219−110, 219, s)-Nets in Base 4

(219−110, 219, 130)-Net over F₄ — Constructive and digital

Digital (109, 219, 130)-net over F₄, using

t-expansion [i] based on digital (105, 219, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 105 and N(F) ≥ 130, using
    - T₇ from the second tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(219−110, 219, 165)-Net over F₄ — Digital

Digital (109, 219, 165)-net over F₄, using

net from sequence [i] based on digital (109, 164)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 109 and N(F) ≥ 165, using
  - Drinfeld modules of rank 1 [i]

(219−110, 219, 1730)-Net in Base 4 — Upper bound on s

There is no (109, 219, 1731)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 717732 386126 587146 339055 314601 146859 462210 388914 057104 065989 361616 474917 140722 590080 845328 172033 566857 816885 903024 851211 570477 334912 > 4²¹⁹ [i]