MinT - Best Known (154−48, 154, s)-Nets in Base 8

Best Known (154−48, 154, s)-Nets in Base 8

(154−48, 154, 1026)-Net over F₈ — Constructive and digital

Digital (106, 154, 1026)-net over F₈, using

2 times m-reduction [i] based on digital (106, 156, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 78, 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]

(154−48, 154, 2412)-Net over F₈ — Digital

Digital (106, 154, 2412)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(154−48, 154, 873141)-Net in Base 8 — Upper bound on s

There is no (106, 154, 873142)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 908651 817164 735041 686307 465907 716323 945267 555313 986815 737280 004598 845334 836797 748337 844460 071455 456037 487727 416582 271730 997547 490876 232756 > 8¹⁵⁴ [i]