MinT - Best Known (36, 72, s)-Nets in Base 8

Best Known (36, 72, s)-Nets in Base 8

(36, 72, 130)-Net over F₈ — Constructive and digital

Digital (36, 72, 130)-net over F₈, using

trace code for nets [i] based on digital (0, 36, 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]

(36, 72, 135)-Net over F₈ — Digital

Digital (36, 72, 135)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(36, 72, 4408)-Net in Base 8 — Upper bound on s

There is no (36, 72, 4409)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 105471 594738 468458 994297 114058 842674 356176 403131 022942 185536 391820 > 8⁷² [i]