MinT - Best Known (61, 61+49, s)-Nets in Base 8

Best Known (61, 61+49, s)-Nets in Base 8

(61, 61+49, 256)-Net over F₈ — Constructive and digital

Digital (61, 110, 256)-net over F₈, using

2 times m-reduction [i] based on digital (61, 112, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 56, 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]

(61, 61+49, 322)-Net over F₈ — Digital

Digital (61, 110, 322)-net over F₈, using

trace code for nets [i] based on digital (6, 55, 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]

(61, 61+49, 17677)-Net in Base 8 — Upper bound on s

There is no (61, 110, 17678)-net in base 8, because

1 times m-reduction [i] would yield (61, 109, 17678)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 273 425096 447525 475591 834260 904409 616676 082902 903951 313518 958199 307458 980365 651203 678442 383901 096304 > 8¹⁰⁹ [i]