MinT - Best Known (157−73, 157, s)-Nets in Base 8

Best Known (157−73, 157, s)-Nets in Base 8

(157−73, 157, 256)-Net over F₈ — Constructive and digital

Digital (84, 157, 256)-net over F₈, using

1 times m-reduction [i] based on 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]

(157−73, 157, 343)-Net over F₈ — Digital

Digital (84, 157, 343)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−73, 157, 16689)-Net in Base 8 — Upper bound on s

There is no (84, 157, 16690)-net in base 8, because

1 times m-reduction [i] would yield (84, 156, 16690)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 763 150672 221799 101828 424160 320237 722928 661620 946846 534382 705765 064371 287680 290901 050088 222796 602569 983344 262430 675335 827818 301218 664860 058804 > 8¹⁵⁶ [i]