MinT - Best Known (20, 68, s)-Nets in Base 4

Best Known (20, 68, s)-Nets in Base 4

(20, 68, 33)-Net over F₄ — Constructive and digital

Digital (20, 68, 33)-net over F₄, using

t-expansion [i] based on digital (15, 68, 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]

(20, 68, 41)-Net over F₄ — Digital

Digital (20, 68, 41)-net over F₄, using

t-expansion [i] based on digital (18, 68, 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]

(20, 68, 116)-Net in Base 4 — Upper bound on s

There is no (20, 68, 117)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶⁸, 117, S₄, 48), but
- the linear programming bound shows that MÂ â‰¥ 17 386566 400310 365130 429344 698706 546300 548809 167457 041405 229063 271574 299683 241127 057478 266601 477863 676931 347562 102784 / 194 255471 902233 779114 903901 006951 502367 530957 736648 427641 695122 360967 936465 > 4⁶⁸ [i]