MinT - Best Known (147, 147+∞, s)-Nets in Base 3

Best Known (147, 147+∞, s)-Nets in Base 3

Digital (147, m, 81)-net over F₃ for arbitrarily large m, using

net from sequence [i] based on digital (147, 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 (147, m, 120)-net over F₃ for arbitrarily large m, using

There is no (147, m, 308)-net in base 3 for arbitrarily large m, because

m-reduction [i] would yield (147, 1841, 308)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3¹⁸⁴¹, 308, S₃, 6, 1694), but
  - the (dual) Plotkin bound for OOAs shows that MÂ â‰¥ 27601 188257 022661 699120 605257 996385 441537 653671 693200 425036 049435 304511 433813 843348 137554 681270 695408 610281 095480 432194 820883 181883 475705 831771 024341 171994 111148 652873 226542 090588 404793 916938 521680 705233 731538 663644 366605 118784 060187 574118 008258 253311 833799 281026 315943 800135 012173 688974 806993 097187 020436 939291 623563 511443 763183 538253 825000 278369 066944 055804 178022 185594 064687 366954 533335 843499 739041 212927 792491 845334 378514 119311 066705 094952 271119 769385 415565 443586 998030 362760 039864 329958 219076 018699 637671 644152 364929 350259 673319 242097 359177 358329 859845 209279 117269 434328 048981 669281 258995 159046 027684 018510 273607 748292 747305 987955 682311 961668 059935 897846 177947 735490 548337 822828 861630 262483 581586 521386 564685 744350 220014 288592 254685 498173 177018 096710 696686 566742 084130 158132 359880 777770 605724 899646 043211 991478 561740 666051 583443 431188 921362 810565 846596 873041 216275 214948 056345 / 113 > 3¹⁸⁴¹ [i]