MinT - Best Known (173−121, 173, s)-Nets in Base 8

Best Known (173−121, 173, s)-Nets in Base 8

(173−121, 173, 98)-Net over F₈ — Constructive and digital

Digital (52, 173, 98)-net over F₈, using

t-expansion [i] based on digital (37, 173, 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]

(173−121, 173, 144)-Net over F₈ — Digital

Digital (52, 173, 144)-net over F₈, using

t-expansion [i] based on digital (45, 173, 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]

(173−121, 173, 1247)-Net in Base 8 — Upper bound on s

There is no (52, 173, 1248)-net in base 8, because

1 times m-reduction [i] would yield (52, 172, 1248)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 216162 693324 720802 770387 272179 057952 067638 762473 575230 915403 802134 739620 146771 466993 230020 272935 713175 405289 064509 814392 370103 900405 913532 943723 785037 500066 > 8¹⁷² [i]