MinT - Best Known (147−73, 147, s)-Nets in Base 8

Best Known (147−73, 147, s)-Nets in Base 8

(147−73, 147, 130)-Net over F₈ — Constructive and digital

Digital (74, 147, 130)-net over F₈, using

1 times m-reduction [i] based on digital (74, 148, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 74, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(147−73, 147, 246)-Net over F₈ — Digital

Digital (74, 147, 246)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(147−73, 147, 9356)-Net in Base 8 — Upper bound on s

There is no (74, 147, 9357)-net in base 8, because

1 times m-reduction [i] would yield (74, 146, 9357)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 710678 759763 725477 165397 514805 928454 057272 266865 232781 092990 088644 219283 057230 390295 530310 059158 521806 305554 349388 993104 282030 867540 > 8¹⁴⁶ [i]