MinT - Best Known (13, 13+31, s)-Nets in Base 4

Best Known (13, 13+31, s)-Nets in Base 4

(13, 13+31, 30)-Net over F₄ — Constructive and digital

Digital (13, 44, 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]

(13, 13+31, 33)-Net over F₄ — Digital

Digital (13, 44, 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]

(13, 13+31, 97)-Net in Base 4 — Upper bound on s

There is no (13, 44, 98)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁴, 98, S₄, 31), but
- the linear programming bound shows that MÂ â‰¥ 3414 029206 960280 274418 067767 340182 249392 781167 507062 000069 867201 406582 128640 000000 / 10 918790 901850 294268 885174 154273 677983 317839 404573 351291 > 4⁴⁴ [i]