MinT - Best Known (146−72, 146, s)-Nets in Base 8

Best Known (146−72, 146, s)-Nets in Base 8

(146−72, 146, 160)-Net over F₈ — Constructive and digital

Digital (74, 146, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 73, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(146−72, 146, 252)-Net over F₈ — Digital

Digital (74, 146, 252)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−72, 146, 9356)-Net in Base 8 — Upper bound on s

There is no (74, 146, 9357)-net in base 8, because

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]