MinT - Best Known (66−47, 66, s)-Nets in Base 4

Best Known (66−47, 66, s)-Nets in Base 4

(66−47, 66, 33)-Net over F₄ — Constructive and digital

Digital (19, 66, 33)-net over F₄, using

t-expansion [i] based on digital (15, 66, 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]

(66−47, 66, 41)-Net over F₄ — Digital

Digital (19, 66, 41)-net over F₄, using

t-expansion [i] based on digital (18, 66, 41)-net over F₄, using
- net from sequence [i] based on digital (18, 40)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 18 and N(F) ≥ 41, using
    - Drinfeld modules of rank 1 [i]

(66−47, 66, 106)-Net in Base 4 — Upper bound on s

There is no (19, 66, 107)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶⁶, 107, S₄, 47), but
- the linear programming bound shows that MÂ â‰¥ 877667 617526 699604 115459 206661 960900 469804 406919 637481 696619 379668 118193 820628 156416 / 152 206215 688292 487856 759376 046017 491747 653675 > 4⁶⁶ [i]