MinT - Best Known (74, 148, s)-Nets in Base 8

Best Known (74, 148, s)-Nets in Base 8

(74, 148, 130)-Net over F₈ — Constructive and digital

Digital (74, 148, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 74, 65)-net over F₆₄, using
- net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
    - the rational function field F₆₄(x) [i]
  - Niederreiter sequence [i]

(74, 148, 241)-Net over F₈ — Digital

Digital (74, 148, 241)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 148, 8550)-Net in Base 8 — Upper bound on s

There is no (74, 148, 8551)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 45 517522 321749 207835 978020 572052 916731 401935 077651 841087 457534 184521 210220 423736 255386 274199 572617 588688 851562 420731 271249 847819 664462 > 8¹⁴⁸ [i]