MinT - Best Known (163−132, 163, s)-Nets in Base 8

Best Known (163−132, 163, s)-Nets in Base 8

(163−132, 163, 65)-Net over F₈ — Constructive and digital

Digital (31, 163, 65)-net over F₈, using

t-expansion [i] based on digital (14, 163, 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]

(163−132, 163, 97)-Net over F₈ — Digital

Digital (31, 163, 97)-net over F₈, using

t-expansion [i] based on digital (28, 163, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(163−132, 163, 576)-Net in Base 8 — Upper bound on s

There is no (31, 163, 577)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1778 719026 808060 603102 145687 591469 468237 888882 383088 290970 361997 971376 949267 052653 721542 557569 063076 511802 631699 934622 155780 499932 009954 514069 673280 > 8¹⁶³ [i]