MinT - Best Known (170−80, 170, s)-Nets in Base 8

Best Known (170−80, 170, s)-Nets in Base 8

(170−80, 170, 256)-Net over F₈ — Constructive and digital

Digital (90, 170, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 85, 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]

(170−80, 170, 349)-Net over F₈ — Digital

Digital (90, 170, 349)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(170−80, 170, 15492)-Net in Base 8 — Upper bound on s

There is no (90, 170, 15493)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3356 853075 845333 282302 992997 257520 108242 509676 519470 547180 573723 047635 450198 918018 741390 782440 052550 188498 235406 418129 534462 322367 117403 272934 368821 027920 > 8¹⁷⁰ [i]