MinT - Best Known (202−88, 202, s)-Nets in Base 3

Best Known (202−88, 202, s)-Nets in Base 3

(202−88, 202, 128)-Net over F₃ — Constructive and digital

Digital (114, 202, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 101, 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]

(202−88, 202, 148)-Net over F₃ — Digital

Digital (114, 202, 148)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(202−88, 202, 1294)-Net in Base 3 — Upper bound on s

There is no (114, 202, 1295)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 419076 609106 599346 265394 762046 593634 716176 760826 807871 763303 730439 651220 163277 860068 707918 885545 > 3²⁰² [i]