MinT - Best Known (163−127, 163, s)-Nets in Base 8

Best Known (163−127, 163, s)-Nets in Base 8

(163−127, 163, 65)-Net over F₈ — Constructive and digital

Digital (36, 163, 65)-net over F₈, using

t-expansion [i] based on digital (14, 163, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(163−127, 163, 112)-Net over F₈ — Digital

Digital (36, 163, 112)-net over F₈, using

t-expansion [i] based on digital (35, 163, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(163−127, 163, 689)-Net in Base 8 — Upper bound on s

There is no (36, 163, 690)-net in base 8, because

1 times m-reduction [i] would yield (36, 162, 690)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 203 679317 907312 233842 529239 231261 962023 179997 111356 618825 219262 934087 289819 168447 498753 753283 713968 165608 173632 966598 221738 891995 321201 439481 497024 > 8¹⁶² [i]