MinT - Best Known (157−43, 157, s)-Nets in Base 8

Best Known (157−43, 157, s)-Nets in Base 8

(157−43, 157, 1026)-Net over F₈ — Constructive and digital

Digital (114, 157, 1026)-net over F₈, using

15 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 86, 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]

(157−43, 157, 5625)-Net over F₈ — Digital

Digital (114, 157, 5625)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−43, 157, 6339603)-Net in Base 8 — Upper bound on s

There is no (114, 157, 6339604)-net in base 8, because

1 times m-reduction [i] would yield (114, 156, 6339604)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 762 146353 993780 810870 209687 540058 496360 959114 811055 479255 175541 397751 781855 163088 211264 356433 274171 520999 814688 450540 528890 762073 725701 515904 > 8¹⁵⁶ [i]