MinT - Best Known (152, ∞, s)-Nets in Base 3

Best Known (152, ∞, s)-Nets in Base 3

Digital (152, m, 81)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (152, 80)-sequence over F₃, using
- t-expansion [i] based on digital (144, 80)-sequence over F₃, using
  - base reduction for sequences [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

Digital (152, m, 163)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (152, 162)-sequence over F₃, using
- t-expansion [i] based on digital (151, 162)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 151 and N(F) ≥ 163, using
    - Drinfeld modules of rank 1 [i]

There is no (152, m, 319)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (152, 1588, 319)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁵⁸⁸, 319, S₃, 5, 1436), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 28669 994563 846126 053711 807707 619627 472599 543071 913697 142417 204433 365949 684382 788518 874617 895870 969041 927664 086220 084302 708430 669723 541265 454169 936744 127724 834509 648995 983513 264283 580851 852026 795768 093004 844019 046287 717296 826553 516245 664044 934115 931006 576880 397670 097893 850882 763417 389466 146652 458846 718967 891937 597303 836532 857179 042593 789976 606385 814696 338692 234218 531973 365603 611348 282632 273131 250176 202330 950816 927682 244297 421371 064042 537782 871343 323235 180154 691415 958621 924794 877041 809047 394839 812495 016329 844617 994848 096517 531939 372978 675705 192472 775669 723520 986933 282173 125063 309618 523537 440557 812588 896323 105726 947739 807153 431615 669233 155473 736993 642254 588380 642907 340721 182209 521970 613485 408299 321127 729453 865425 688162 079374 968299 583391 671438 790231 949015 / 479 > 3¹⁵⁸⁸ [i]