MinT - Best Known (128−34, 128, s)-Nets in Base 8

Best Known (128−34, 128, s)-Nets in Base 8

(128−34, 128, 1026)-Net over F₈ — Constructive and digital

Digital (94, 128, 1026)-net over F₈, using

4 times m-reduction [i] based on digital (94, 132, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 66, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(128−34, 128, 6003)-Net over F₈ — Digital

Digital (94, 128, 6003)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−34, 128, 6465213)-Net in Base 8 — Upper bound on s

There is no (94, 128, 6465214)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 39 402107 714238 126216 135241 823716 774408 638005 507264 581489 556376 362080 419931 377324 933271 166077 294351 293246 472117 835727 > 8¹²⁸ [i]