MinT - Best Known (94, 94+68, s)-Nets in Base 3

Best Known (94, 94+68, s)-Nets in Base 3

(94, 94+68, 128)-Net over F₃ — Constructive and digital

Digital (94, 162, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 81, 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]

(94, 94+68, 136)-Net over F₃ — Digital

Digital (94, 162, 136)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(94, 94+68, 1236)-Net in Base 3 — Upper bound on s

There is no (94, 162, 1237)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 197590 506525 659571 256100 187004 865461 698590 922484 421429 399710 259647 654386 392049 > 3¹⁶² [i]