MinT - Best Known (63, 63+61, s)-Nets in Base 8

Best Known (63, 63+61, s)-Nets in Base 8

(63, 63+61, 160)-Net over F₈ — Constructive and digital

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+61, 222)-Net over F₈ — Digital

Digital (63, 124, 222)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(63, 63+61, 8658)-Net in Base 8 — Upper bound on s

There is no (63, 124, 8659)-net in base 8, because

1 times m-reduction [i] would yield (63, 123, 8659)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1206 507491 307280 195243 271296 577491 905169 024751 166042 756640 532204 769880 499319 467406 316227 726784 240806 546103 854320 > 8¹²³ [i]