MinT - Best Known (84, 84+74, s)-Nets in Base 8

Best Known (84, 84+74, s)-Nets in Base 8

(84, 84+74, 256)-Net over F₈ — Constructive and digital

Digital (84, 158, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 79, 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]

(84, 84+74, 335)-Net over F₈ — Digital

Digital (84, 158, 335)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(84, 84+74, 15016)-Net in Base 8 — Upper bound on s

There is no (84, 158, 15017)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 48792 608974 207313 702677 452799 723375 415500 399064 803248 453649 332768 994867 720809 710198 997341 932872 365278 949278 053180 861630 707041 277932 681372 669176 > 8¹⁵⁸ [i]