MinT - Best Known (64, 64+60, s)-Nets in Base 9

Best Known (64, 64+60, s)-Nets in Base 9

(64, 64+60, 232)-Net over F₉ — Constructive and digital

Digital (64, 124, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 62, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(64, 64+60, 272)-Net over F₉ — Digital

Digital (64, 124, 272)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+60, 13222)-Net in Base 9 — Upper bound on s

There is no (64, 124, 13223)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21227 642665 066863 373120 839433 235056 150085 603363 185614 491771 816163 145689 484794 337349 850932 107788 756615 199594 450366 723473 > 9¹²⁴ [i]