MinT - Best Known (17, 17+36, s)-Nets in Base 4

Best Known (17, 17+36, s)-Nets in Base 4

(17, 17+36, 33)-Net over F₄ — Constructive and digital

Digital (17, 53, 33)-net over F₄, using

t-expansion [i] based on digital (15, 53, 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]

(17, 17+36, 40)-Net over F₄ — Digital

Digital (17, 53, 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]

(17, 17+36, 133)-Net in Base 4 — Upper bound on s

There is no (17, 53, 134)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁵³, 134, S₄, 36), but
- the linear programming bound shows that MÂ â‰¥ 13977 135218 163528 704731 898937 416611 213183 957686 665072 733824 249885 272036 744364 032000 / 160 460837 511194 840278 088549 800082 466977 532904 587207 > 4⁵³ [i]