MinT - Best Known (106, 106+81, s)-Nets in Base 3

Best Known (106, 106+81, s)-Nets in Base 3

(106, 106+81, 80)-Net over F₃ — Constructive and digital

Digital (106, 187, 80)-net over F₃, using

9 times m-reduction [i] based on digital (106, 196, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 98, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(106, 106+81, 141)-Net over F₃ — Digital

Digital (106, 187, 141)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+81, 1265)-Net in Base 3 — Upper bound on s

There is no (106, 187, 1266)-net in base 3, because

1 times m-reduction [i] would yield (106, 186, 1266)-net in base 3, but
- 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]