MinT - Best Known (131−71, 131, s)-Nets in Base 8

Best Known (131−71, 131, s)-Nets in Base 8

(131−71, 131, 113)-Net over F₈ — Constructive and digital

Digital (60, 131, 113)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (11, 46, 48)-net over F₈, using
  - net from sequence [i] based on digital (11, 47)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 11 and N(F) ≥ 48, using
      - a function field by SÃ©mirat [i]
2. digital (14, 85, 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]

(131−71, 131, 158)-Net over F₈ — Digital

Digital (60, 131, 158)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−71, 131, 4470)-Net in Base 8 — Upper bound on s

There is no (60, 131, 4471)-net in base 8, because

1 times m-reduction [i] would yield (60, 130, 4471)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2528 494907 800234 197383 345587 843031 552770 592965 317811 148345 281769 548233 450257 085707 807561 909778 888703 797014 039868 792164 > 8¹³⁰ [i]