MinT - Best Known (85, 85+126, s)-Nets in Base 4

Best Known (85, 85+126, s)-Nets in Base 4

(85, 85+126, 104)-Net over F₄ — Constructive and digital

Digital (85, 211, 104)-net over F₄, using

t-expansion [i] based on digital (73, 211, 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+126, 129)-Net over F₄ — Digital

Digital (85, 211, 129)-net over F₄, using

t-expansion [i] based on digital (81, 211, 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+126, 790)-Net in Base 4 — Upper bound on s

There is no (85, 211, 791)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11 218732 908550 643638 836932 642913 660470 591025 816672 407339 935896 526551 646703 357156 708468 642815 510397 650764 343986 893355 177070 583680 > 4²¹¹ [i]