MinT - Best Known (106−92, 106, s)-Nets in Base 9

Best Known (106−92, 106, s)-Nets in Base 9

Digital (14, 106, 64)-net over F₉, using

t-expansion [i] based on digital (13, 106, 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, 106, 245)-net over F₉, because

2 times m-reduction [i] would yield digital (14, 104, 245)-net over F₉, but
- 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, 106, 296)-net in base 9, because

1 times m-reduction [i] would yield (14, 105, 296)-net in base 9, but
- extracting embedded orthogonal array [i] would yield OA(9¹⁰⁵, 296, S₉, 91), but
  - 4 times code embedding in larger space [i] would yield OA(9¹⁰⁹, 300, S₉, 91), but
    - the linear programming bound shows that MÂ â‰¥ 20222 799818 611528 390839 277680 990437 852821 899749 659618 739342 348854 851621 934809 018713 731640 335873 496606 947807 631043 020745 250556 108238 860543 808208 661623 549467 241197 146341 789454 357912 244440 307783 758391 874756 943996 955708 885548 663018 102772 250563 951855 296962 004991 487605 675937 656784 820992 176169 210657 583602 018134 843407 006374 499626 056694 666348 761036 941407 872455 758028 390625 / 143 054740 270656 633488 392262 718105 773360 612686 977272 532344 200031 604422 144964 478577 760888 042608 628665 041022 318137 588353 699588 796466 027052 526379 998082 508571 490419 781784 580497 514796 342636 447960 946621 294322 436053 645032 848773 074025 656095 538373 258490 431688 098827 929153 > 9¹⁰⁹ [i]