MinT - Best Known (14, 14+31, s)-Nets in Base 4

Best Known (14, 14+31, s)-Nets in Base 4

(14, 14+31, 30)-Net over F₄ — Constructive and digital

Digital (14, 45, 30)-net over F₄, using

t-expansion [i] based on digital (13, 45, 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+31, 33)-Net over F₄ — Digital

Digital (14, 45, 33)-net over F₄, using

t-expansion [i] based on digital (13, 45, 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+31, 111)-Net in Base 4 — Upper bound on s

There is no (14, 45, 112)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁵, 112, S₄, 31), but
- the linear programming bound shows that MÂ â‰¥ 30 703316 954186 650166 302103 088413 940385 262854 668690 715040 548493 721600 / 24108 147423 127287 645158 347013 987588 540153 > 4⁴⁵ [i]