MinT - Best Known (33, 117, s)-Nets in Base 4

Best Known (33, 117, s)-Nets in Base 4

(33, 117, 56)-Net over F₄ — Constructive and digital

Digital (33, 117, 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]

(33, 117, 65)-Net over F₄ — Digital

Digital (33, 117, 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]

(33, 117, 140)-Net in Base 4 — Upper bound on s

There is no (33, 117, 141)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4¹¹⁷, 141, S₄, 84), but
- the linear programming bound shows that MÂ â‰¥ 252 139606 714309 522794 950236 846768 949351 023280 026733 448193 800335 971345 511185 130977 230848 / 7950 715750 039425 > 4¹¹⁷ [i]