MinT - Best Known (47−33, 47, s)-Nets in Base 4

Best Known (47−33, 47, s)-Nets in Base 4

(47−33, 47, 30)-Net over F₄ — Constructive and digital

Digital (14, 47, 30)-net over F₄, using

t-expansion [i] based on digital (13, 47, 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]

(47−33, 47, 33)-Net over F₄ — Digital

Digital (14, 47, 33)-net over F₄, using

t-expansion [i] based on digital (13, 47, 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]

(47−33, 47, 103)-Net in Base 4 — Upper bound on s

There is no (14, 47, 104)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁷, 104, S₄, 33), but
- the linear programming bound shows that MÂ â‰¥ 1174 046639 191630 223681 185273 503735 047219 518200 396804 079380 889257 898555 970298 959666 030187 642880 / 54879 229485 183725 296974 155563 481145 282045 055361 543282 990010 805653 > 4⁴⁷ [i]