MinT - Best Known (34, 34+87, s)-Nets in Base 4

Best Known (34, 34+87, s)-Nets in Base 4

(34, 34+87, 56)-Net over F₄ — Constructive and digital

Digital (34, 121, 56)-net over F₄, using

t-expansion [i] based on digital (33, 121, 56)-net over F₄, using
- net from sequence [i] based on digital (33, 55)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 56, using
    - F₅ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(34, 34+87, 65)-Net over F₄ — Digital

Digital (34, 121, 65)-net over F₄, using

t-expansion [i] based on digital (33, 121, 65)-net over F₄, using
- net from sequence [i] based on digital (33, 64)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 33 and N(F) ≥ 65, using
    - Drinfeld modules of rank 1 [i]

(34, 34+87, 144)-Net in Base 4 — Upper bound on s

There is no (34, 121, 145)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4¹²¹, 145, S₄, 87), but
- the linear programming bound shows that MÂ â‰¥ 241502 590268 189986 517960 819451 991263 770225 532833 261695 725476 600361 862422 859217 680809 852928 / 21697 738822 577169 > 4¹²¹ [i]