MinT - Best Known (141−126, 141, s)-Nets in Base 9

Best Known (141−126, 141, s)-Nets in Base 9

(141−126, 141, 64)-Net over F₉ — Constructive and digital

Digital (15, 141, 64)-net over F₉, using

t-expansion [i] based on digital (13, 141, 64)-net over F₉, using
- net from sequence [i] based on digital (13, 63)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
    - a function field by GarcÃa and Quoos [i]

(141−126, 141, 135)-Net in Base 9 — Upper bound on s

There is no (15, 141, 136)-net in base 9, because

18 times m-reduction [i] would yield (15, 123, 136)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9¹²³, 136, S₉, 108), but
  - the linear programming bound shows that MÂ â‰¥ 43937 926141 213657 416061 906681 876494 817263 274556 001188 989748 982782 114241 968389 523142 886351 436942 916837 719711 850478 384204 731164 785821 / 15 367369 428125 > 9¹²³ [i]