MinT - Best Known (40, 40+125, s)-Nets in Base 8

Best Known (40, 40+125, s)-Nets in Base 8

(40, 40+125, 98)-Net over F₈ — Constructive and digital

Digital (40, 165, 98)-net over F₈, using

t-expansion [i] based on digital (37, 165, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(40, 40+125, 129)-Net over F₈ — Digital

Digital (40, 165, 129)-net over F₈, using

t-expansion [i] based on digital (38, 165, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(40, 40+125, 798)-Net in Base 8 — Upper bound on s

There is no (40, 165, 799)-net in base 8, because

1 times m-reduction [i] would yield (40, 164, 799)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13587 925016 988601 532317 595239 966370 298364 906019 545579 643242 424182 432411 810763 512110 234634 345210 560803 212685 773422 389980 334745 602175 944439 463115 564152 > 8¹⁶⁴ [i]