MinT - Best Known (43, 43+32, s)-Nets in Base 8

Best Known (43, 43+32, s)-Nets in Base 8

(43, 43+32, 256)-Net over F₈ — Constructive and digital

Digital (43, 75, 256)-net over F₈, using

1 times m-reduction [i] based on digital (43, 76, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 38, 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]

(43, 43+32, 276)-Net over F₈ — Digital

Digital (43, 75, 276)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 43+32, 16611)-Net in Base 8 — Upper bound on s

There is no (43, 75, 16612)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 53 925124 072188 628123 448320 305521 280324 054901 495284 698295 841092 900490 > 8⁷⁵ [i]