MinT - Best Known (106−50, 106, s)-Nets in Base 8

Best Known (106−50, 106, s)-Nets in Base 8

(106−50, 106, 208)-Net over F₈ — Constructive and digital

Digital (56, 106, 208)-net over F₈, using

trace code for nets [i] based on digital (3, 53, 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]

(106−50, 106, 232)-Net over F₈ — Digital

Digital (56, 106, 232)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−50, 106, 9793)-Net in Base 8 — Upper bound on s

There is no (56, 106, 9794)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 534623 092224 970065 131551 657891 734290 621523 612272 254853 054719 698452 108424 614302 485780 895650 202680 > 8¹⁰⁶ [i]