MinT - Best Known (70, 70+64, s)-Nets in Base 8

Best Known (70, 70+64, s)-Nets in Base 8

(70, 70+64, 208)-Net over F₈ — Constructive and digital

Digital (70, 134, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 67, 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]

(70, 70+64, 268)-Net over F₈ — Digital

Digital (70, 134, 268)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+64, 11032)-Net in Base 8 — Upper bound on s

There is no (70, 134, 11033)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 10 337290 813029 171600 113239 637271 350560 112200 750065 233898 416898 139878 408156 212196 283591 165182 694025 892779 858101 828419 903640 > 8¹³⁴ [i]