MinT - Best Known (242−108, 242, s)-Nets in Base 3

Best Known (242−108, 242, s)-Nets in Base 3

(242−108, 242, 128)-Net over F₃ — Constructive and digital

Digital (134, 242, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 121, 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]

(242−108, 242, 163)-Net over F₃ — Digital

Digital (134, 242, 163)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(242−108, 242, 1388)-Net in Base 3 — Upper bound on s

There is no (134, 242, 1389)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 604687 332288 184366 040821 895432 123848 406386 457157 229688 402065 394255 748827 509813 631680 281976 854814 781617 547635 232017 > 3²⁴² [i]