MinT - Best Known (105−90, 105, s)-Nets in Base 8

Best Known (105−90, 105, s)-Nets in Base 8

(105−90, 105, 65)-Net over F₈ — Constructive and digital

Digital (15, 105, 65)-net over F₈, using

t-expansion [i] based on digital (14, 105, 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]

(105−90, 105, 127)-Net in Base 8 — Upper bound on s

There is no (15, 105, 128)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8¹⁰⁵, 128, S₈, 90), but
- the linear programming bound shows that MÂ â‰¥ 21950 796382 814438 782744 864463 381336 127596 030073 856912 690696 782531 039738 810829 256630 497562 292754 935128 215485 677031 129088 / 296811 395949 608374 280875 > 8¹⁰⁵ [i]