MinT - Best Known (78, 78+67, s)-Nets in Base 8

Best Known (78, 78+67, s)-Nets in Base 8

(78, 78+67, 256)-Net over F₈ — Constructive and digital

Digital (78, 145, 256)-net over F₈, using

1 times m-reduction [i] based on digital (78, 146, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 73, 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]

(78, 78+67, 329)-Net over F₈ — Digital

Digital (78, 145, 329)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+67, 16385)-Net in Base 8 — Upper bound on s

There is no (78, 145, 16386)-net in base 8, because

1 times m-reduction [i] would yield (78, 144, 16386)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11098 286551 525501 901312 992918 761618 401022 239324 478203 969709 463273 309868 797490 565923 168324 821124 115979 311993 317738 800146 490439 475712 > 8¹⁴⁴ [i]