MinT - Best Known (62−45, 62, s)-Nets in Base 4

Best Known (62−45, 62, s)-Nets in Base 4

(62−45, 62, 33)-Net over F₄ — Constructive and digital

Digital (17, 62, 33)-net over F₄, using

t-expansion [i] based on digital (15, 62, 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]

(62−45, 62, 40)-Net over F₄ — Digital

Digital (17, 62, 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]

(62−45, 62, 87)-Net in Base 4 — Upper bound on s

There is no (17, 62, 88)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶², 88, S₄, 45), but
- the linear programming bound shows that MÂ â‰¥ 1 115878 796922 411753 730265 232586 868317 882698 851925 622784 / 45512 145087 655961 > 4⁶² [i]