MinT - Best Known (106, 106+89, s)-Nets in Base 3

Best Known (106, 106+89, s)-Nets in Base 3

(106, 106+89, 80)-Net over F₃ — Constructive and digital

Digital (106, 195, 80)-net over F₃, using

1 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+89, 126)-Net over F₃ — Digital

Digital (106, 195, 126)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+89, 1052)-Net in Base 3 — Upper bound on s

There is no (106, 195, 1053)-net in base 3, because

1 times m-reduction [i] would yield (106, 194, 1053)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 370 516930 661693 781273 837722 823758 665611 225709 302303 859878 927778 899983 999204 861310 740812 802161 > 3¹⁹⁴ [i]