MinT - Best Known (86, 86+160, s)-Nets in Base 4

Best Known (86, 86+160, s)-Nets in Base 4

(86, 86+160, 104)-Net over F₄ — Constructive and digital

Digital (86, 246, 104)-net over F₄, using

t-expansion [i] based on digital (73, 246, 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]

(86, 86+160, 129)-Net over F₄ — Digital

Digital (86, 246, 129)-net over F₄, using

t-expansion [i] based on digital (81, 246, 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]

(86, 86+160, 660)-Net in Base 4 — Upper bound on s

There is no (86, 246, 661)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 13819 293742 863698 315178 227092 953733 026135 896749 497257 463796 566610 184137 085723 911027 909774 247182 618221 029001 140345 961879 698333 739235 863492 226378 523950 > 4²⁴⁶ [i]