MinT - Best Known (128−60, 128, s)-Nets in Base 9

Best Known (128−60, 128, s)-Nets in Base 9

(128−60, 128, 300)-Net over F₉ — Constructive and digital

Digital (68, 128, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 64, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(128−60, 128, 319)-Net over F₉ — Digital

Digital (68, 128, 319)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(128−60, 128, 17729)-Net in Base 9 — Upper bound on s

There is no (68, 128, 17730)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 139 219984 940956 715417 520934 772260 898533 064956 854618 576594 214476 249245 943063 358859 055639 964947 068517 506463 252192 722095 799329 > 9¹²⁸ [i]