MinT - Best Known (186−80, 186, s)-Nets in Base 3

Best Known (186−80, 186, s)-Nets in Base 3

(186−80, 186, 128)-Net over F₃ — Constructive and digital

Digital (106, 186, 128)-net over F₃, using

trace code for nets [i] based on digital (13, 93, 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]

(186−80, 186, 143)-Net over F₃ — Digital

Digital (106, 186, 143)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(186−80, 186, 1265)-Net in Base 3 — Upper bound on s

There is no (106, 186, 1266)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 56767 098669 424778 155749 677347 544441 307531 910665 999193 192510 479031 062221 415586 344486 466705 > 3¹⁸⁶ [i]