MinT - Best Known (107, 107+91, s)-Nets in Base 3

Best Known (107, 107+91, s)-Nets in Base 3

(107, 107+91, 80)-Net over F₃ — Constructive and digital

Digital (107, 198, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 99, 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]

(107, 107+91, 126)-Net over F₃ — Digital

Digital (107, 198, 126)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(107, 107+91, 1037)-Net in Base 3 — Upper bound on s

There is no (107, 198, 1038)-net in base 3, because

1 times m-reduction [i] would yield (107, 197, 1038)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 10099 625886 517040 190397 646750 322751 823737 536961 513834 257371 111044 559709 742483 988802 294785 500005 > 3¹⁹⁷ [i]