MinT - Best Known (213−132, 213, s)-Nets in Base 4

Best Known (213−132, 213, s)-Nets in Base 4

(213−132, 213, 104)-Net over F₄ — Constructive and digital

Digital (81, 213, 104)-net over F₄, using

t-expansion [i] based on digital (73, 213, 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]

(213−132, 213, 129)-Net over F₄ — Digital

Digital (81, 213, 129)-net over F₄, using

net from sequence [i] based on digital (81, 128)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 81 and N(F) ≥ 129, using
  - Drinfeld modules of rank 1 [i]

(213−132, 213, 689)-Net in Base 4 — Upper bound on s

There is no (81, 213, 690)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 174 001245 507460 340996 059709 390312 043748 400061 363878 503288 226981 282303 128959 840300 099778 220370 985184 042587 063189 096309 713839 625280 > 4²¹³ [i]