MinT - Best Known (162−76, 162, s)-Nets in Base 8

Best Known (162−76, 162, s)-Nets in Base 8

(162−76, 162, 256)-Net over F₈ — Constructive and digital

Digital (86, 162, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 81, 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]

(162−76, 162, 339)-Net over F₈ — Digital

Digital (86, 162, 339)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(162−76, 162, 15171)-Net in Base 8 — Upper bound on s

There is no (86, 162, 15172)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 199 906912 449778 247127 017108 146602 458270 208447 286308 015214 977955 164361 171760 431452 219917 183878 735609 415210 320848 220523 197595 673944 831070 311900 454800 > 8¹⁶² [i]