MinT - Best Known (138−125, 138, s)-Nets in Base 9

Best Known (138−125, 138, s)-Nets in Base 9

(138−125, 138, 64)-Net over F₉ — Constructive and digital

Digital (13, 138, 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]

(138−125, 138, 120)-Net in Base 9 — Upper bound on s

There is no (13, 138, 121)-net in base 9, because

32 times m-reduction [i] would yield (13, 106, 121)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9¹⁰⁶, 121, S₉, 93), but
  - the linear programming bound shows that MÂ â‰¥ 14386 856892 109753 589943 480991 392045 806312 525494 995317 258231 047340 377435 156302 384720 183485 695337 425818 836413 178517 / 99301 439965 > 9¹⁰⁶ [i]