MinT - Best Known (172−156, 172, s)-Nets in Base 8

Best Known (172−156, 172, s)-Nets in Base 8

(172−156, 172, 65)-Net over F₈ — Constructive and digital

Digital (16, 172, 65)-net over F₈, using

t-expansion [i] based on digital (14, 172, 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]

(172−156, 172, 129)-Net in Base 8 — Upper bound on s

There is no (16, 172, 130)-net in base 8, because

58 times m-reduction [i] would yield (16, 114, 130)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8¹¹⁴, 130, S₈, 98), but
  - the linear programming bound shows that MÂ â‰¥ 35521 613223 977817 808600 584786 921883 743646 382533 111114 232182 834553 852288 928742 958552 390470 329316 634829 110683 210776 313856 / 3847 120524 212625 > 8¹¹⁴ [i]