MinT - Best Known (5, 5+26, s)-Nets in Base 64

Best Known (5, 5+26, s)-Nets in Base 64

(5, 5+26, 128)-Net over F₆₄ — Constructive and digital

Digital (5, 31, 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]

(5, 5+26, 129)-Net in Base 64 — Constructive

(5, 31, 129)-net in base 64, using

4 times m-reduction [i] based on (5, 35, 129)-net in base 64, using
- base change [i] based on digital (0, 30, 129)-net over F₁₂₈, using
  - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
      - the rational function field F₁₂₈(x) [i]
    - Niederreiter sequence [i]

(5, 5+26, 133)-Net over F₆₄ — Digital

Digital (5, 31, 133)-net over F₆₄, using

net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
  - a curve from the manYPoints database [i]

(5, 5+26, 1818)-Net in Base 64 — Upper bound on s

There is no (5, 31, 1819)-net in base 64, because

the generalized Rao bound for nets shows that 64^mÂ â‰¥ 98 670756 327852 165013 938762 178995 829520 998538 356638 382120 > 64³¹ [i]