MinT - Best Known (61−41, 61, s)-Nets in Base 4

Best Known (61−41, 61, s)-Nets in Base 4

(61−41, 61, 33)-Net over F₄ — Constructive and digital

Digital (20, 61, 33)-net over F₄, using

t-expansion [i] based on digital (15, 61, 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]

(61−41, 61, 41)-Net over F₄ — Digital

Digital (20, 61, 41)-net over F₄, using

t-expansion [i] based on digital (18, 61, 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]

(61−41, 61, 154)-Net in Base 4 — Upper bound on s

There is no (20, 61, 155)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶¹, 155, S₄, 41), but
- the linear programming bound shows that MÂ â‰¥ 35 162266 348965 864492 465363 741528 241521 515995 482555 223491 846236 883313 207330 736210 116983 129154 519040 / 6 178619 757792 266774 478203 941876 542733 832278 327110 913669 619231 > 4⁶¹ [i]