MinT - Best Known (30−15, 30, s)-Nets in Base 4

Best Known (30−15, 30, s)-Nets in Base 4

(30−15, 30, 34)-Net over F₄ — Constructive and digital

Digital (15, 30, 34)-net over F₄, using

trace code for nets [i] based on digital (0, 15, 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]

(30−15, 30, 36)-Net over F₄ — Digital

Digital (15, 30, 36)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(30−15, 30, 346)-Net in Base 4 — Upper bound on s

There is no (15, 30, 347)-net in base 4, because

1 times m-reduction [i] would yield (15, 29, 347)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 292293 108172 922560 > 4²⁹ [i]