MinT - Best Known (113−51, 113, s)-Nets in Base 8

Best Known (113−51, 113, s)-Nets in Base 8

(113−51, 113, 256)-Net over F₈ — Constructive and digital

Digital (62, 113, 256)-net over F₈, using

1 times m-reduction [i] based on digital (62, 114, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 57, 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]

(113−51, 113, 294)-Net over F₈ — Digital

Digital (62, 113, 294)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(113−51, 113, 16141)-Net in Base 8 — Upper bound on s

There is no (62, 113, 16142)-net in base 8, because

1 times m-reduction [i] would yield (62, 112, 16142)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 140024 592394 279129 216099 753634 713027 137476 775015 148349 058160 814266 056976 692841 713645 545980 643183 851248 > 8¹¹² [i]