MinT - Best Known (18−10, 18, s)-Nets in Base 8

Best Known (18−10, 18, s)-Nets in Base 8

(18−10, 18, 36)-Net over F₈ — Constructive and digital

Digital (8, 18, 36)-net over F₈, using

8¹ times duplication [i] based on digital (7, 17, 36)-net over F₈, using
- Niederreiter sequence (Bratleyâ€“Foxâ€“Niederreiter implementation) [i]

(18−10, 18, 38)-Net in Base 8 — Constructive

(8, 18, 38)-net in base 8, using

2 times m-reduction [i] based on (8, 20, 38)-net in base 8, using
- base change [i] based on digital (3, 15, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(18−10, 18, 42)-Net over F₈ — Digital

Digital (8, 18, 42)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(18−10, 18, 660)-Net in Base 8 — Upper bound on s

There is no (8, 18, 661)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 18038 558092 380792 > 8¹⁸ [i]