MinT - Best Known (106, 106+39, s)-Nets in Base 3

Best Known (106, 106+39, s)-Nets in Base 3

(106, 106+39, 264)-Net over F₃ — Constructive and digital

Digital (106, 145, 264)-net over F₃, using

3¹ times duplication [i] based on digital (105, 144, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 48, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(106, 106+39, 496)-Net over F₃ — Digital

Digital (106, 145, 496)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(106, 106+39, 16359)-Net in Base 3 — Upper bound on s

There is no (106, 145, 16360)-net in base 3, because

1 times m-reduction [i] would yield (106, 144, 16360)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 507 784299 592510 871571 250244 584250 140212 901408 557660 750074 639591 947041 > 3¹⁴⁴ [i]