MinT - Best Known (85, 85+107, s)-Nets in Base 4

Best Known (85, 85+107, s)-Nets in Base 4

(85, 85+107, 104)-Net over F₄ — Constructive and digital

Digital (85, 192, 104)-net over F₄, using

t-expansion [i] based on digital (73, 192, 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]

(85, 85+107, 129)-Net over F₄ — Digital

Digital (85, 192, 129)-net over F₄, using

t-expansion [i] based on digital (81, 192, 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]

(85, 85+107, 971)-Net in Base 4 — Upper bound on s

There is no (85, 192, 972)-net in base 4, because

1 times m-reduction [i] would yield (85, 191, 972)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 9 962988 161563 657593 805926 690057 552382 417215 479954 103187 523805 513311 481495 601265 018625 404458 745148 757165 448842 575400 > 4¹⁹¹ [i]