MinT - Best Known (104−90, 104, s)-Nets in Base 9

Best Known (104−90, 104, s)-Nets in Base 9

Digital (14, 104, 64)-net over F₉, using

t-expansion [i] based on digital (13, 104, 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]

There is no digital (14, 104, 245)-net over F₉, because

extracting embedded orthogonal array [i] would yield linear OA(9¹⁰⁴, 245, F₉, 90) (dual of [245, 141, 91]-code), but
- residual code [i] would yield OA(9¹⁴, 154, S₉, 10), but
  - the linear programming bound shows that MÂ â‰¥ 9 845183 946168 672136 787115 / 427681 338151 > 9¹⁴ [i]

There is no (14, 104, 297)-net in base 9, because

6 times m-reduction [i] would yield (14, 98, 297)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9⁹⁸, 297, S₉, 84), but
  - 3 times code embedding in larger space [i] would yield OA(9¹⁰¹, 300, S₉, 84), but
    - the linear programming bound shows that MÂ â‰¥ 1 081998 669707 713617 008118 839294 498618 821381 818821 191631 819083 846833 140437 910265 005393 444184 161924 063086 216407 548641 525677 495826 651979 260620 122496 177412 740362 341175 579757 321258 116751 578963 540482 706106 154392 879092 133039 203814 443162 745573 656874 574966 467765 281228 145475 364040 247610 203586 272313 854193 414553 / 333490 034521 302951 507456 531016 579021 531798 114410 969477 904264 373430 475441 890592 220587 254122 250696 405667 929332 288616 723146 874441 254966 478154 141391 882461 295760 569172 601427 866250 799306 856867 123574 444844 101549 > 9¹⁰¹ [i]