MinT - Best Known (65, 65+63, s)-Nets in Base 8

Best Known (65, 65+63, s)-Nets in Base 8

(65, 65+63, 160)-Net over F₈ — Constructive and digital

Digital (65, 128, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 64, 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]

(65, 65+63, 227)-Net over F₈ — Digital

Digital (65, 128, 227)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+63, 8866)-Net in Base 8 — Upper bound on s

There is no (65, 128, 8867)-net in base 8, because

1 times m-reduction [i] would yield (65, 127, 8867)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 937903 673965 569341 581191 851130 459176 781625 406196 882428 322164 887560 208107 040469 555731 274683 688274 812560 646453 024480 > 8¹²⁷ [i]