MinT - Best Known (246−110, 246, s)-Nets in Base 3

Best Known (246−110, 246, s)-Nets in Base 3

(246−110, 246, 128)-Net over F₃ — Constructive and digital

Digital (136, 246, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 123, 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]

(246−110, 246, 164)-Net over F₃ — Digital

Digital (136, 246, 164)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(246−110, 246, 1398)-Net in Base 3 — Upper bound on s

There is no (136, 246, 1399)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2355 388931 447020 818471 419825 888334 937530 527917 444900 293875 296642 569384 117662 533318 152020 348755 682976 751102 088643 116019 > 3²⁴⁶ [i]