MinT - Best Known (158−115, 158, s)-Nets in Base 8

Best Known (158−115, 158, s)-Nets in Base 8

(158−115, 158, 98)-Net over F₈ — Constructive and digital

Digital (43, 158, 98)-net over F₈, using

t-expansion [i] based on digital (37, 158, 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]

(158−115, 158, 129)-Net over F₈ — Digital

Digital (43, 158, 129)-net over F₈, using

t-expansion [i] based on digital (38, 158, 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]

(158−115, 158, 933)-Net in Base 8 — Upper bound on s

There is no (43, 158, 934)-net in base 8, because

1 times m-reduction [i] would yield (43, 157, 934)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6341 920620 304016 845944 296085 796999 153132 347676 798905 483194 939373 541341 245296 952467 455917 917799 729617 904613 923064 713892 369809 640302 570368 762640 > 8¹⁵⁷ [i]