MinT - Best Known (41, 41+107, s)-Nets in Base 8

Best Known (41, 41+107, s)-Nets in Base 8

(41, 41+107, 98)-Net over F₈ — Constructive and digital

Digital (41, 148, 98)-net over F₈, using

t-expansion [i] based on digital (37, 148, 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]

(41, 41+107, 129)-Net over F₈ — Digital

Digital (41, 148, 129)-net over F₈, using

t-expansion [i] based on digital (38, 148, 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]

(41, 41+107, 907)-Net in Base 8 — Upper bound on s

There is no (41, 148, 908)-net in base 8, because

1 times m-reduction [i] would yield (41, 147, 908)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 817587 411654 091253 200688 884601 986805 826399 653458 296983 658583 719316 727988 379230 595154 995361 691594 848317 577984 622297 346444 804667 062896 > 8¹⁴⁷ [i]