Best Known (13, ∞, s)-Nets in Base 27
(13, ∞, 96)-Net over F27 — Constructive and digital
Digital (13, m, 96)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (13, 95)-sequence over F27, using
- t-expansion [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- t-expansion [i] based on digital (11, 95)-sequence over F27, using
(13, ∞, 136)-Net over F27 — Digital
Digital (13, m, 136)-net over F27 for arbitrarily large m, using
- net from sequence [i] based on digital (13, 135)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 13 and N(F) ≥ 136, using
(13, ∞, 391)-Net in Base 27 — Upper bound on s
There is no (13, m, 392)-net in base 27 for arbitrarily large m, because
- m-reduction [i] would yield (13, 781, 392)-net in base 27, but
- extracting embedded OOA [i] would yield OOA(27781, 392, S27, 2, 768), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 86945 564006 957549 719381 490614 240611 193434 515527 036420 418508 924469 043509 324803 981779 902513 580085 813933 189110 601289 546005 506942 124578 376743 371596 276366 220078 285930 767811 355956 719753 863140 577347 803684 656729 097552 162912 561478 227949 220161 727004 015594 427320 815819 780959 146073 958628 080325 910432 215774 810392 178052 545915 705353 281435 613579 837389 411175 341789 990876 499747 349773 703772 056522 019038 674568 919188 608947 284557 108343 669575 916741 231510 715668 082347 851741 945382 561170 939984 297335 146964 022102 587585 447219 890674 693694 119725 578866 539872 741559 808779 981160 710213 215456 104122 883799 137440 638597 226373 636306 249869 176610 482391 654080 556803 293470 939041 268845 634067 044965 065045 122187 768815 177658 825288 760553 003313 527582 179737 766905 235626 763806 068294 503707 896697 021810 552125 577484 430459 797865 911113 915876 261722 770960 357261 220485 189718 075496 344071 729655 801166 630571 371701 320245 040733 492309 039559 531326 206414 457116 920209 039512 619844 964810 561190 961762 724426 767955 331002 802743 709163 876145 229805 639059 330731 772368 332244 375214 866521 026672 645073 784245 120933 170087 592008 460000 222944 832420 122562 226277 541610 469320 836844 590518 309490 195449 931468 467089 / 769 > 27781 [i]
- extracting embedded OOA [i] would yield OOA(27781, 392, S27, 2, 768), but