MinT - Best Known (148−43, 148, s)-Nets in Base 8

Best Known (148−43, 148, s)-Nets in Base 8

(148−43, 148, 1026)-Net over F₈ — Constructive and digital

Digital (105, 148, 1026)-net over F₈, using

6 times m-reduction [i] based on digital (105, 154, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 77, 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]

(148−43, 148, 3610)-Net over F₈ — Digital

Digital (105, 148, 3610)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(148−43, 148, 2600292)-Net in Base 8 — Upper bound on s

There is no (105, 148, 2600293)-net in base 8, because

1 times m-reduction [i] would yield (105, 147, 2600293)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 678433 555215 344635 808515 610645 315380 379233 149341 537474 499760 727546 029086 518437 734933 053317 312046 629562 724738 546931 801899 378382 744816 > 8¹⁴⁷ [i]