MinT - Best Known (142−42, 142, s)-Nets in Base 8

Best Known (142−42, 142, s)-Nets in Base 8

(142−42, 142, 1026)-Net over F₈ — Constructive and digital

Digital (100, 142, 1026)-net over F₈, using

2 times m-reduction [i] based on digital (100, 144, 1026)-net over F₈, using
- trace code for nets [i] based on digital (28, 72, 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]

(142−42, 142, 3115)-Net over F₈ — Digital

Digital (100, 142, 3115)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(142−42, 142, 1584891)-Net in Base 8 — Upper bound on s

There is no (100, 142, 1584892)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 293739 760864 990904 633621 079574 725672 534164 344839 186542 473297 412535 284615 298638 000775 968801 066469 953257 091586 936050 455931 800650 > 8¹⁴² [i]