Best Known (146, ∞, s)-Nets in Base 3
(146, ∞, 81)-Net over F3 — Constructive and digital
Digital (146, m, 81)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (146, 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
- Niederreiter–Xing sequence construction 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]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- base reduction for sequences [i] based on digital (32, 80)-sequence over F9, using
- t-expansion [i] based on digital (144, 80)-sequence over F3, using
(146, ∞, 120)-Net over F3 — Digital
Digital (146, m, 120)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (146, 119)-sequence over F3, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 113 and N(F) ≥ 120, using
- t-expansion [i] based on digital (113, 119)-sequence over F3, using
(146, ∞, 305)-Net in Base 3 — Upper bound on s
There is no (146, m, 306)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (146, 1829, 306)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(31829, 306, S3, 6, 1683), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 195100 610817 263446 136891 329365 195817 650898 240921 691950 811924 123869 802536 702836 256213 241121 736184 227191 314728 678991 102503 875174 078772 726538 817799 685651 821327 068107 082462 078144 436896 318254 185808 696929 499408 982202 084919 834013 417248 149694 919203 343486 457300 093785 852024 614090 200177 241795 070827 799707 783583 859384 738834 870531 040072 192484 183906 748045 412795 005668 052928 856441 983483 886999 318004 516532 030949 605446 062192 127777 236745 925628 122691 206616 841828 343556 814716 141736 566930 177436 633316 606398 052316 832762 900315 303095 943061 807416 951796 749394 367488 937413 540829 874167 886419 698442 464916 219340 330543 525276 742780 215522 243279 624537 604811 902080 942632 427007 807085 328091 275207 184820 168297 415516 442245 144710 708087 228389 248804 435066 194665 235384 592520 172988 816555 815011 209130 433450 657209 530220 309345 631782 201957 412641 849106 905933 773641 340397 764049 460070 331724 238663 233579 869430 459151 225358 205456 / 421 > 31829 [i]
- extracting embedded OOA [i] would yield OOA(31829, 306, S3, 6, 1683), but