MinT - Best Known (98, 98+35, s)-Nets in Base 3

Best Known (98, 98+35, s)-Nets in Base 3

(98, 98+35, 264)-Net over F₃ — Constructive and digital

Digital (98, 133, 264)-net over F₃, using

3¹ times duplication [i] based on digital (97, 132, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 44, 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]

(98, 98+35, 505)-Net over F₃ — Digital

Digital (98, 133, 505)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(98, 98+35, 18164)-Net in Base 3 — Upper bound on s

There is no (98, 133, 18165)-net in base 3, because

1 times m-reduction [i] would yield (98, 132, 18165)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 955 309158 051653 848838 481480 697216 738793 309082 058705 363993 040811 > 3¹³² [i]