Best Known (72, 72+108, s)-Nets in Base 3
(72, 72+108, 48)-Net over F3 — Constructive and digital
Digital (72, 180, 48)-net over F3, using
- t-expansion [i] based on digital (45, 180, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(72, 72+108, 84)-Net over F3 — Digital
Digital (72, 180, 84)-net over F3, using
- t-expansion [i] based on digital (71, 180, 84)-net over F3, using
- net from sequence [i] based on digital (71, 83)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 71 and N(F) ≥ 84, using
- net from sequence [i] based on digital (71, 83)-sequence over F3, using
(72, 72+108, 295)-Net in Base 3 — Upper bound on s
There is no (72, 180, 296)-net in base 3, because
- 1 times m-reduction [i] would yield (72, 179, 296)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3179, 296, S3, 107), but
- 4 times code embedding in larger space [i] would yield OA(3183, 300, S3, 107), but
- the linear programming bound shows that M ≥ 309631 848141 006597 816000 452264 526609 584728 332967 128301 572177 140277 632424 449938 823859 038961 200634 916556 688139 195773 157569 537913 350697 096510 344035 302998 314235 032997 759550 042700 153610 202325 169537 169318 898231 014029 626476 635670 186192 072079 231985 324401 931189 206163 503394 476760 209500 664729 580647 297125 187274 791328 367699 877409 028050 828009 356248 814296 906965 210354 545517 689804 127653 161292 918322 701831 971334 709435 128724 889329 / 137 689303 746583 388514 280861 964087 994239 553595 524780 210680 513306 492357 023800 962068 841716 406921 103502 736303 501710 566956 675237 994820 955505 230289 044190 752861 590766 354890 407967 225346 405560 766155 870216 667429 550336 168210 482382 321060 653356 122593 034299 157947 141074 347113 813964 534922 826766 642372 918146 039195 166785 843274 520716 686796 800000 > 3183 [i]
- 4 times code embedding in larger space [i] would yield OA(3183, 300, S3, 107), but
- extracting embedded orthogonal array [i] would yield OA(3179, 296, S3, 107), but