MinT - Best Known (128−61, 128, s)-Nets in Base 8

Best Known (128−61, 128, s)-Nets in Base 8

(128−61, 128, 208)-Net over F₈ — Constructive and digital

Digital (67, 128, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 64, 104)-net over F₆₄, using
- net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(128−61, 128, 261)-Net over F₈ — Digital

Digital (67, 128, 261)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−61, 128, 11430)-Net in Base 8 — Upper bound on s

There is no (67, 128, 11431)-net in base 8, because

1 times m-reduction [i] would yield (67, 127, 11431)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 933908 787680 691260 059468 833460 253041 745164 733343 706730 861760 444837 856800 213205 002107 139473 583510 684540 931362 381300 > 8¹²⁷ [i]