MinT - Best Known (60, 60+65, s)-Nets in Base 8

Best Known (60, 60+65, s)-Nets in Base 8

(60, 60+65, 130)-Net over F₈ — Constructive and digital

Digital (60, 125, 130)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (14, 46, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
      - the Suzuki function field over F₈ [i]
2. digital (14, 79, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(60, 60+65, 178)-Net over F₈ — Digital

Digital (60, 125, 178)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+65, 5751)-Net in Base 8 — Upper bound on s

There is no (60, 125, 5752)-net in base 8, because

1 times m-reduction [i] would yield (60, 124, 5752)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 9672 268550 187291 974020 507628 305364 284932 360747 968919 816506 112607 905915 634028 634535 573426 550883 175329 192057 116449 > 8¹²⁴ [i]