MinT - Best Known (157−139, 157, s)-Nets in Base 8

Best Known (157−139, 157, s)-Nets in Base 8

(157−139, 157, 65)-Net over F₈ — Constructive and digital

Digital (18, 157, 65)-net over F₈, using

t-expansion [i] based on digital (14, 157, 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]

(157−139, 157, 143)-Net in Base 8 — Upper bound on s

There is no (18, 157, 144)-net in base 8, because

29 times m-reduction [i] would yield (18, 128, 144)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8¹²⁸, 144, S₈, 110), but
  - the linear programming bound shows that MÂ â‰¥ 6109 893966 434273 613815 828543 318095 703793 603744 881950 919851 825987 742070 359262 466307 770153 217353 472069 496822 008994 926770 763501 404160 / 124 535855 141787 > 8¹²⁸ [i]