MinT - Best Known (72, 128, s)-Nets in Base 3

Best Known (72, 128, s)-Nets in Base 3

(72, 128, 80)-Net over F₃ — Constructive and digital

Digital (72, 128, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 64, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(72, 128, 100)-Net over F₃ — Digital

Digital (72, 128, 100)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 128, 830)-Net in Base 3 — Upper bound on s

There is no (72, 128, 831)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 12 142275 025307 033315 939458 065484 971514 769984 822743 173894 581193 > 3¹²⁸ [i]