MinT - Best Known (64, 64+62, s)-Nets in Base 9

Best Known (64, 64+62, s)-Nets in Base 9

(64, 64+62, 200)-Net over F₉ — Constructive and digital

Digital (64, 126, 200)-net over F₉, using

trace code for nets [i] based on digital (1, 63, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(64, 64+62, 256)-Net over F₉ — Digital

Digital (64, 126, 256)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(64, 64+62, 11715)-Net in Base 9 — Upper bound on s

There is no (64, 126, 11716)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1 716287 479461 108362 646762 949696 124268 117655 362806 993352 563420 576716 625572 669974 035629 065888 163937 722458 302140 611191 005281 > 9¹²⁶ [i]