MinT - Best Known (171−127, 171, s)-Nets in Base 8

Best Known (171−127, 171, s)-Nets in Base 8

(171−127, 171, 98)-Net over F₈ — Constructive and digital

Digital (44, 171, 98)-net over F₈, using

t-expansion [i] based on digital (37, 171, 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]

(171−127, 171, 130)-Net over F₈ — Digital

Digital (44, 171, 130)-net over F₈, using

net from sequence [i] based on digital (44, 129)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 44 and N(F) ≥ 130, using
  - a curve from the manYPoints database [i]

(171−127, 171, 909)-Net in Base 8 — Upper bound on s

There is no (44, 171, 910)-net in base 8, because

1 times m-reduction [i] would yield (44, 170, 910)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3358 093947 363236 516325 689996 105109 351706 240697 466660 549745 931551 085925 622770 570716 592992 728499 933530 521421 121856 242254 645090 220803 141753 788751 267170 630976 > 8¹⁷⁰ [i]