MinT - Best Known (131−35, 131, s)-Nets in Base 8

Best Known (131−35, 131, s)-Nets in Base 8

(131−35, 131, 1026)-Net over F₈ — Constructive and digital

Digital (96, 131, 1026)-net over F₈, using

5 times m-reduction [i] based on digital (96, 136, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 68, 513)-net over F₆₄, using
  - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
      - the Hermitian function field over F₆₄ [i]

(131−35, 131, 5850)-Net over F₈ — Digital

Digital (96, 131, 5850)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−35, 131, 8257125)-Net in Base 8 — Upper bound on s

There is no (96, 131, 8257126)-net in base 8, because

1 times m-reduction [i] would yield (96, 130, 8257126)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2521 732350 897022 130964 319428 633218 870826 746033 440662 022035 008610 652586 062079 547404 510796 109239 419761 195315 080165 142398 > 8¹³⁰ [i]