MinT - Best Known (178−76, 178, s)-Nets in Base 3

Best Known (178−76, 178, s)-Nets in Base 3

(178−76, 178, 128)-Net over F₃ — Constructive and digital

Digital (102, 178, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 89, 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]

(178−76, 178, 141)-Net over F₃ — Digital

Digital (102, 178, 141)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−76, 178, 1253)-Net in Base 3 — Upper bound on s

There is no (102, 178, 1254)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 639462 109299 212643 964554 122122 236406 860087 785632 940316 142610 655637 376737 172287 959125 > 3¹⁷⁸ [i]