MinT - Best Known (36−18, 36, s)-Nets in Base 4

Best Known (36−18, 36, s)-Nets in Base 4

(36−18, 36, 34)-Net over F₄ — Constructive and digital

Digital (18, 36, 34)-net over F₄, using

trace code for nets [i] based on digital (0, 18, 17)-net over F₁₆, using
- net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
    - the rational function field F₁₆(x) [i]
  - Niederreiter sequence [i]

(36−18, 36, 41)-Net over F₄ — Digital

Digital (18, 36, 41)-net over F₄, using

net from sequence [i] based on digital (18, 40)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 18 and N(F) ≥ 41, using
  - Drinfeld modules of rank 1 [i]

(36−18, 36, 346)-Net in Base 4 — Upper bound on s

There is no (18, 36, 347)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 4728 897123 261325 268014 > 4³⁶ [i]