MinT - Best Known (127−81, 127, s)-Nets in Base 8

Best Known (127−81, 127, s)-Nets in Base 8

(127−81, 127, 98)-Net over F₈ — Constructive and digital

Digital (46, 127, 98)-net over F₈, using

t-expansion [i] based on digital (37, 127, 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]

(127−81, 127, 144)-Net over F₈ — Digital

Digital (46, 127, 144)-net over F₈, using

t-expansion [i] based on digital (45, 127, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(127−81, 127, 1550)-Net in Base 8 — Upper bound on s

There is no (46, 127, 1551)-net in base 8, because

1 times m-reduction [i] would yield (46, 126, 1551)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 624510 191656 326189 868427 414510 531492 922327 986493 559271 131981 670292 404616 001128 948389 372160 503718 840851 365398 445104 > 8¹²⁶ [i]