MinT - Best Known (151−47, 151, s)-Nets in Base 8

Best Known (151−47, 151, s)-Nets in Base 8

(151−47, 151, 1026)-Net over F₈ — Constructive and digital

Digital (104, 151, 1026)-net over F₈, using

1 times m-reduction [i] based on digital (104, 152, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 76, 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]

(151−47, 151, 2392)-Net over F₈ — Digital

Digital (104, 151, 2392)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(151−47, 151, 1044887)-Net in Base 8 — Upper bound on s

There is no (104, 151, 1044888)-net in base 8, because

1 times m-reduction [i] would yield (104, 150, 1044888)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2907 375408 807026 466390 455978 189106 261484 063174 761015 373135 895084 583257 099684 645481 382447 458960 809002 259961 328140 284007 346954 275604 577559 > 8¹⁵⁰ [i]