MinT - Best Known (113−99, 113, s)-Nets in Base 9

Best Known (113−99, 113, s)-Nets in Base 9

(113−99, 113, 64)-Net over F₉ — Constructive and digital

Digital (14, 113, 64)-net over F₉, using

t-expansion [i] based on digital (13, 113, 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]

(113−99, 113, 129)-Net in Base 9 — Upper bound on s

There is no (14, 113, 130)-net in base 9, because

1 times m-reduction [i] would yield (14, 112, 130)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9¹¹², 130, S₉, 98), but
  - the linear programming bound shows that MÂ â‰¥ 102044 798726 074157 946342 526694 215757 184839 498802 434893 273680 913908 810135 229505 295636 373747 351906 016797 225362 681955 238106 940191 / 1 306729 034666 969375 > 9¹¹² [i]