MinT - Best Known (13, 13+∞, s)-Nets in Base 32

Best Known (13, 13+∞, s)-Nets in Base 32

Digital (13, m, 120)-net over F₃₂ for arbitrarily large m, using

net from sequence [i] based on digital (13, 119)-sequence over F₃₂, using
- t-expansion [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

Digital (13, m, 129)-net over F₃₂ for arbitrarily large m, using

net from sequence [i] based on digital (13, 128)-sequence over F₃₂, using
- t-expansion [i] based on digital (12, 128)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

There is no (13, m, 463)-net in base 32 for arbitrarily large m, because

m-reduction [i] would yield (13, 461, 463)-net in base 32, but
- extracting embedded OOA [i] would yield OA(32⁴⁶¹, 463, S₃₂, 448), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 3 592371 504856 448095 073279 782596 789560 856891 670586 472834 573368 105966 185204 299974 558849 207472 138171 853801 633274 922045 016400 880653 418865 578498 163095 749789 335689 133977 454466 296499 229455 071350 996929 017658 992731 346431 107224 843787 202412 150960 858049 188280 899203 422639 232738 100867 170306 684393 780802 510982 259105 970229 376589 488767 642306 788003 157392 973459 461648 613981 503433 573772 780341 464978 025014 302393 551829 130044 373034 967430 879250 741886 163563 687075 699538 987713 833333 244256 972747 949340 894291 827347 329336 448369 299686 659214 593212 437613 919286 271975 378894 308175 721228 515336 127965 616840 390615 601044 521168 467459 956629 932593 566989 328402 154508 412061 432031 284932 940980 342127 071995 139477 102702 377483 643317 841674 895360 / 449 > 32⁴⁶¹ [i]