MinT - Best Known (99, 99+41, s)-Nets in Base 8

Best Known (99, 99+41, s)-Nets in Base 8

(99, 99+41, 1026)-Net over F₈ — Constructive and digital

Digital (99, 140, 1026)-net over F₈, using

2 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+41, 3282)-Net over F₈ — Digital

Digital (99, 140, 3282)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(99, 99+41, 2242235)-Net in Base 8 — Upper bound on s

There is no (99, 140, 2242236)-net in base 8, because

1 times m-reduction [i] would yield (99, 139, 2242236)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 338462 433829 606257 743326 016047 176965 435319 072725 281367 912292 449699 483296 138613 728552 096996 664230 566953 468959 085139 185520 874954 > 8¹³⁹ [i]