MinT - Best Known (43−37, 43, s)-Nets in Base 64

Best Known (43−37, 43, s)-Nets in Base 64

(43−37, 43, 128)-Net over F₆₄ — Constructive and digital

Digital (6, 43, 128)-net over F₆₄, using

t-expansion [i] based on digital (5, 43, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(43−37, 43, 161)-Net over F₆₄ — Digital

Digital (6, 43, 161)-net over F₆₄, using

net from sequence [i] based on digital (6, 160)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
  - a curve from the manYPoints database [i]

(43−37, 43, 1955)-Net in Base 64 — Upper bound on s

There is no (6, 43, 1956)-net in base 64, because

1 times m-reduction [i] would yield (6, 42, 1956)-net in base 64, but
- the generalized Rao bound for nets shows that 64^mÂ â‰¥ 7268 253839 045773 987658 216937 652645 408160 936325 936390 832875 410330 639708 415802 > 64⁴² [i]