MinT - Best Known (80, 80+54, s)-Nets in Base 3

Best Known (80, 80+54, s)-Nets in Base 3

(80, 80+54, 128)-Net over F₃ — Constructive and digital

Digital (80, 134, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 67, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(80, 80+54, 131)-Net over F₃ — Digital

Digital (80, 134, 131)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+54, 1248)-Net in Base 3 — Upper bound on s

There is no (80, 134, 1249)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8752 000423 581064 428058 236976 964960 143773 890603 631384 938150 105147 > 3¹³⁴ [i]