MinT - Best Known (46−32, 46, s)-Nets in Base 4

Best Known (46−32, 46, s)-Nets in Base 4

(46−32, 46, 30)-Net over F₄ — Constructive and digital

Digital (14, 46, 30)-net over F₄, using

t-expansion [i] based on digital (13, 46, 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]

(46−32, 46, 33)-Net over F₄ — Digital

Digital (14, 46, 33)-net over F₄, using

t-expansion [i] based on digital (13, 46, 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]

(46−32, 46, 107)-Net in Base 4 — Upper bound on s

There is no (14, 46, 108)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁶, 108, S₄, 32), but
- the linear programming bound shows that MÂ â‰¥ 7521 585930 885377 473826 532410 438434 365147 619053 743009 472248 914222 591788 142097 858560 000000 / 1 441569 793884 706534 073896 273915 521544 945772 995787 416063 963723 > 4⁴⁶ [i]