MinT - Best Known (110−61, 110, s)-Nets in Base 8

Best Known (110−61, 110, s)-Nets in Base 8

(110−61, 110, 98)-Net over F₈ — Constructive and digital

Digital (49, 110, 98)-net over F₈, using

t-expansion [i] based on digital (37, 110, 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]

(110−61, 110, 144)-Net over F₈ — Digital

Digital (49, 110, 144)-net over F₈, using

t-expansion [i] based on digital (45, 110, 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]

(110−61, 110, 3269)-Net in Base 8 — Upper bound on s

There is no (49, 110, 3270)-net in base 8, because

1 times m-reduction [i] would yield (49, 109, 3270)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 275 561209 484075 010415 867641 138466 648888 441138 590361 270337 443233 294136 046092 347973 376381 147477 072352 > 8¹⁰⁹ [i]