MinT - Best Known (63−47, 63, s)-Nets in Base 4

Best Known (63−47, 63, s)-Nets in Base 4

(63−47, 63, 33)-Net over F₄ — Constructive and digital

Digital (16, 63, 33)-net over F₄, using

t-expansion [i] based on digital (15, 63, 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]

(63−47, 63, 36)-Net over F₄ — Digital

Digital (16, 63, 36)-net over F₄, using

net from sequence [i] based on digital (16, 35)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 16 and N(F) ≥ 36, using
  - Drinfeld modules of rank 1 [i]

(63−47, 63, 74)-Net in Base 4 — Upper bound on s

There is no (16, 63, 75)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶³, 75, S₄, 47), but
- the linear programming bound shows that MÂ â‰¥ 108 051901 662607 115934 306119 345453 950792 892416 / 1 213839 > 4⁶³ [i]