MinT - Best Known (158−87, 158, s)-Nets in Base 8

Best Known (158−87, 158, s)-Nets in Base 8

(158−87, 158, 130)-Net over F₈ — Constructive and digital

Digital (71, 158, 130)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (14, 57, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]
2. digital (14, 101, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(158−87, 158, 173)-Net over F₈ — Digital

Digital (71, 158, 173)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−87, 158, 4755)-Net in Base 8 — Upper bound on s

There is no (71, 158, 4756)-net in base 8, because

1 times m-reduction [i] would yield (71, 157, 4756)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6103 239800 649057 175814 820850 938050 886376 812082 628726 123788 472737 606862 807732 254305 993186 673767 396679 046430 948572 795093 697781 257649 370968 605656 > 8¹⁵⁷ [i]