MinT - Best Known (116−30, 116, s)-Nets in Base 8

Best Known (116−30, 116, s)-Nets in Base 8

(116−30, 116, 1026)-Net over F₈ — Constructive and digital

Digital (86, 116, 1026)-net over F₈, using

trace code for nets [i] based on digital (28, 58, 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]

(116−30, 116, 6844)-Net over F₈ — Digital

Digital (86, 116, 6844)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(116−30, 116, large)-Net in Base 8 — Upper bound on s

There is no (86, 116, large)-net in base 8, because

28 times m-reduction [i] would yield (86, 88, large)-net in base 8, but
- mutually orthogonal hypercube bound [i]