MinT - Best Known (147−104, 147, s)-Nets in Base 8

Best Known (147−104, 147, s)-Nets in Base 8

(147−104, 147, 98)-Net over F₈ — Constructive and digital

Digital (43, 147, 98)-net over F₈, using

t-expansion [i] based on digital (37, 147, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(147−104, 147, 129)-Net over F₈ — Digital

Digital (43, 147, 129)-net over F₈, using

t-expansion [i] based on digital (38, 147, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(147−104, 147, 999)-Net in Base 8 — Upper bound on s

There is no (43, 147, 1000)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 797328 693257 213084 997672 692624 424763 647441 875026 656054 040715 662731 349763 484188 403680 033352 355008 727190 788577 905007 462555 318323 151116 > 8¹⁴⁷ [i]