MinT - Best Known (35−18, 35, s)-Nets in Base 4

Best Known (35−18, 35, s)-Nets in Base 4

(35−18, 35, 33)-Net over F₄ — Constructive and digital

Digital (17, 35, 33)-net over F₄, using

t-expansion [i] based on digital (15, 35, 33)-net over F₄, using
- net from sequence [i] based on digital (15, 32)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
    - an explicitly constructive algebraic function field [i]

(35−18, 35, 40)-Net over F₄ — Digital

Digital (17, 35, 40)-net over F₄, using

net from sequence [i] based on digital (17, 39)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 17 and N(F) ≥ 40, using
  - Drinfeld modules of rank 1 [i]

(35−18, 35, 296)-Net in Base 4 — Upper bound on s

There is no (17, 35, 297)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1200 552285 689017 416244 > 4³⁵ [i]