MinT - Best Known (221−132, 221, s)-Nets in Base 4

Best Known (221−132, 221, s)-Nets in Base 4

(221−132, 221, 104)-Net over F₄ — Constructive and digital

Digital (89, 221, 104)-net over F₄, using

t-expansion [i] based on digital (73, 221, 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]

(221−132, 221, 129)-Net over F₄ — Digital

Digital (89, 221, 129)-net over F₄, using

t-expansion [i] based on digital (81, 221, 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]

(221−132, 221, 825)-Net in Base 4 — Upper bound on s

There is no (89, 221, 826)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 629740 200319 585721 108542 150602 131104 026554 268582 493831 266368 550598 150796 240560 808540 918346 578910 740276 284653 410460 064386 186949 824560 > 4²²¹ [i]