MinT - Best Known (99, 99+37, s)-Nets in Base 8

Best Known (99, 99+37, s)-Nets in Base 8

(99, 99+37, 1026)-Net over F₈ — Constructive and digital

Digital (99, 136, 1026)-net over F₈, using

6 times m-reduction [i] based on digital (99, 142, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 71, 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]

(99, 99+37, 5282)-Net over F₈ — Digital

Digital (99, 136, 5282)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+37, 6400386)-Net in Base 8 — Upper bound on s

There is no (99, 136, 6400387)-net in base 8, because

1 times m-reduction [i] would yield (99, 135, 6400387)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 82 632224 095835 948661 147284 081541 729762 947190 861718 057570 946895 012225 702377 139173 349362 982835 153225 116834 262271 229067 409576 > 8¹³⁵ [i]