MinT - Best Known (83, 185, s)-Nets in Base 4

Best Known (83, 185, s)-Nets in Base 4

(83, 185, 104)-Net over F₄ — Constructive and digital

Digital (83, 185, 104)-net over F₄, using

t-expansion [i] based on digital (73, 185, 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]

(83, 185, 129)-Net over F₄ — Digital

Digital (83, 185, 129)-net over F₄, using

t-expansion [i] based on digital (81, 185, 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]

(83, 185, 969)-Net in Base 4 — Upper bound on s

There is no (83, 185, 970)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2468 598184 050857 088161 996220 813524 604436 591316 053728 186565 618646 070647 723632 011729 752483 177902 523249 107898 093680 > 4¹⁸⁵ [i]