MinT - Best Known (119, 119+49, s)-Nets in Base 8

Best Known (119, 119+49, s)-Nets in Base 8

(119, 119+49, 1026)-Net over F₈ — Constructive and digital

Digital (119, 168, 1026)-net over F₈, using

t-expansion [i] based on digital (114, 168, 1026)-net over F₈, using
- 4 times m-reduction [i] based on digital (114, 172, 1026)-net over F₈, using
  - trace code for nets [i] based on digital (28, 86, 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]

(119, 119+49, 3901)-Net over F₈ — Digital

Digital (119, 168, 3901)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+49, 2693168)-Net in Base 8 — Upper bound on s

There is no (119, 168, 2693169)-net in base 8, because

1 times m-reduction [i] would yield (119, 167, 2693169)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 546838 538779 501452 767348 919027 236184 904363 058087 907455 401178 214862 962150 155072 476127 666535 351239 721588 990618 367985 008679 132958 314289 018231 365641 948444 > 8¹⁶⁷ [i]