MinT - Best Known (102−46, 102, s)-Nets in Base 8

Best Known (102−46, 102, s)-Nets in Base 8

(102−46, 102, 256)-Net over F₈ — Constructive and digital

Digital (56, 102, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 51, 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]

(102−46, 102, 271)-Net over F₈ — Digital

Digital (56, 102, 271)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−46, 102, 13611)-Net in Base 8 — Upper bound on s

There is no (56, 102, 13612)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 130 448586 958616 261841 254354 403516 749656 038093 724018 711873 888467 207787 431942 877056 676309 812564 > 8¹⁰² [i]