MinT - Best Known (12, 42, s)-Nets in Base 4

Best Known (12, 42, s)-Nets in Base 4

(12, 42, 28)-Net over F₄ — Constructive and digital

Digital (12, 42, 28)-net over F₄, using

net from sequence [i] based on digital (12, 27)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 28, using
  - an explicitly constructive algebraic function field [i]

(12, 42, 29)-Net over F₄ — Digital

Digital (12, 42, 29)-net over F₄, using

net from sequence [i] based on digital (12, 28)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 12 and N(F) ≥ 29, using
  - a curve from the manYPoints database [i]

(12, 42, 87)-Net in Base 4 — Upper bound on s

There is no (12, 42, 88)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴², 88, S₄, 30), but
- the linear programming bound shows that MÂ â‰¥ 89 605050 492137 134852 017163 586838 439030 395196 856884 186345 777644 655144 707653 985466 546419 715121 697993 523200 / 4 627392 744873 205288 863270 778823 516250 097275 954094 267550 824480 805099 989747 440773 > 4⁴² [i]