MinT - Best Known (63, 63+59, s)-Nets in Base 8

Best Known (63, 63+59, s)-Nets in Base 8

(63, 63+59, 160)-Net over F₈ — Constructive and digital

Digital (63, 122, 160)-net over F₈, using

2 times m-reduction [i] based on digital (63, 124, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 62, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(63, 63+59, 235)-Net over F₈ — Digital

Digital (63, 122, 235)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+59, 9756)-Net in Base 8 — Upper bound on s

There is no (63, 122, 9757)-net in base 8, because

1 times m-reduction [i] would yield (63, 121, 9757)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 18 830475 139082 653582 557328 855541 663935 326440 205805 715926 083464 106829 190309 220067 437560 455780 339957 719048 741096 > 8¹²¹ [i]