MinT - Best Known (106−48, 106, s)-Nets in Base 8

Best Known (106−48, 106, s)-Nets in Base 8

(106−48, 106, 256)-Net over F₈ — Constructive and digital

Digital (58, 106, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 53, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(106−48, 106, 275)-Net over F₈ — Digital

Digital (58, 106, 275)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−48, 106, 13628)-Net in Base 8 — Upper bound on s

There is no (58, 106, 13629)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 534798 177388 215563 655621 696770 572423 599709 711168 092741 756458 546074 574804 173272 361710 800035 667833 > 8¹⁰⁶ [i]