MinT - Best Known (45−32, 45, s)-Nets in Base 4

Best Known (45−32, 45, s)-Nets in Base 4

(45−32, 45, 30)-Net over F₄ — Constructive and digital

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]

(45−32, 45, 33)-Net over F₄ — Digital

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]

(45−32, 45, 93)-Net in Base 4 — Upper bound on s

There is no (13, 45, 94)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁵, 94, S₄, 32), but
- the linear programming bound shows that MÂ â‰¥ 5620 184626 019067 545133 732595 852193 606492 239172 450795 055293 610024 696241 375244 513537 251173 048636 372484 511737 707886 460600 729196 298240 / 4 490354 977671 109171 977374 825515 463646 543995 191995 384881 187906 235255 501379 117691 433461 827076 002203 266473 > 4⁴⁵ [i]