MinT - Best Known (34−18, 34, s)-Nets in Base 8

Best Known (34−18, 34, s)-Nets in Base 8

(34−18, 34, 65)-Net over F₈ — Constructive and digital

Digital (16, 34, 65)-net over F₈, using

t-expansion [i] based on digital (14, 34, 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]

(34−18, 34, 66)-Net over F₈ — Digital

Digital (16, 34, 66)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(8³⁴, 66, F₈, 2, 18) (dual of [(66, 2), 98, 19]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(8³², 65, F₈, 2, 18) (dual of [(65, 2), 98, 19]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,111P) [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(34−18, 34, 1523)-Net in Base 8 — Upper bound on s

There is no (16, 34, 1524)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 087467 372139 671713 659541 403818 > 8³⁴ [i]