MinT - Best Known (77, 77+67, s)-Nets in Base 8

Best Known (77, 77+67, s)-Nets in Base 8

(77, 77+67, 256)-Net over F₈ — Constructive and digital

Digital (77, 144, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 72, 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]

(77, 77+67, 318)-Net over F₈ — Digital

Digital (77, 144, 318)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(77, 77+67, 15383)-Net in Base 8 — Upper bound on s

There is no (77, 144, 15384)-net in base 8, because

1 times m-reduction [i] would yield (77, 143, 15384)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1387 113730 852741 376948 312642 317433 171958 471859 651217 609458 979184 423057 924013 760409 259103 780270 470267 223349 497758 674483 138033 144160 > 8¹⁴³ [i]