MinT - Best Known (163, 163+74, s)-Nets in Base 3

Best Known (163, 163+74, s)-Nets in Base 3

(163, 163+74, 204)-Net over F₃ — Constructive and digital

Digital (163, 237, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 79, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(163, 163+74, 454)-Net over F₃ — Digital

Digital (163, 237, 454)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163, 163+74, 8301)-Net in Base 3 — Upper bound on s

There is no (163, 237, 8302)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 120087 609800 056056 250867 508355 169160 308251 235980 293453 647577 914284 331490 189690 426028 137370 819172 868392 571611 632693 > 3²³⁷ [i]