MinT - Best Known (60−43, 60, s)-Nets in Base 4

Best Known (60−43, 60, s)-Nets in Base 4

(60−43, 60, 33)-Net over F₄ — Constructive and digital

Digital (17, 60, 33)-net over F₄, using

t-expansion [i] based on digital (15, 60, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(60−43, 60, 40)-Net over F₄ — Digital

Digital (17, 60, 40)-net over F₄, using

net from sequence [i] based on digital (17, 39)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 17 and N(F) ≥ 40, using
  - Drinfeld modules of rank 1 [i]

(60−43, 60, 96)-Net in Base 4 — Upper bound on s

There is no (17, 60, 97)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶⁰, 97, S₄, 43), but
- the linear programming bound shows that MÂ â‰¥ 397 009202 024702 523768 652504 484945 932069 120818 488153 315427 343594 355263 799296 / 269 558632 232160 195053 526197 508114 230285 > 4⁶⁰ [i]