MinT - Best Known (14, 14+34, s)-Nets in Base 4

Best Known (14, 14+34, s)-Nets in Base 4

(14, 14+34, 30)-Net over F₄ — Constructive and digital

Digital (14, 48, 30)-net over F₄, using

t-expansion [i] based on digital (13, 48, 30)-net over F₄, using
- net from sequence [i] based on digital (13, 29)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 30, using
    - F₄ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(14, 14+34, 33)-Net over F₄ — Digital

Digital (14, 48, 33)-net over F₄, using

t-expansion [i] based on digital (13, 48, 33)-net over F₄, using
- net from sequence [i] based on digital (13, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 13 and N(F) ≥ 33, using
    - Drinfeld modules of rank 1 [i]

(14, 14+34, 99)-Net in Base 4 — Upper bound on s

There is no (14, 48, 100)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁸, 100, S₄, 34), but
- the linear programming bound shows that MÂ â‰¥ 9058 957890 512598 877597 243353 229194 029550 244654 789588 151723 066658 722038 162924 682285 684121 927080 009184 894902 538211 707610 394949 320704 / 112877 238751 180015 015346 131872 600873 922049 184597 216985 800847 416342 964009 902792 675071 874309 392551 306831 > 4⁴⁸ [i]