MinT - Best Known (146−68, 146, s)-Nets in Base 8

Best Known (146−68, 146, s)-Nets in Base 8

(146−68, 146, 256)-Net over F₈ — Constructive and digital

Digital (78, 146, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 73, 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]

(146−68, 146, 321)-Net over F₈ — Digital

Digital (78, 146, 321)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−68, 146, 14578)-Net in Base 8 — Upper bound on s

There is no (78, 146, 14579)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 710423 600674 405549 850001 598411 426436 721006 980712 854200 650348 757261 891013 974235 686409 245874 405287 785883 196248 960870 877726 229107 336661 > 8¹⁴⁶ [i]