MinT - Best Known (72, 72+72, s)-Nets in Base 8

Best Known (72, 72+72, s)-Nets in Base 8

(72, 72+72, 130)-Net over F₈ — Constructive and digital

Digital (72, 144, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 72, 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]

(72, 72+72, 235)-Net over F₈ — Digital

Digital (72, 144, 235)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+72, 8333)-Net in Base 8 — Upper bound on s

There is no (72, 144, 8334)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11120 019013 332389 818786 544037 248143 806246 747153 478706 868713 287160 035019 425719 382859 636019 184545 603600 893917 045690 195920 049350 868356 > 8¹⁴⁴ [i]