Best Known (106−95, 106, s)-Nets in Base 27
(106−95, 106, 96)-Net over F27 — Constructive and digital
Digital (11, 106, 96)-net over F27, using
- net from sequence [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
(106−95, 106, 100)-Net over F27 — Digital
Digital (11, 106, 100)-net over F27, using
- net from sequence [i] based on digital (11, 99)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 100, using
(106−95, 106, 1069)-Net over F27 — Upper bound on s (digital)
There is no digital (11, 106, 1070)-net over F27, because
- 17 times m-reduction [i] would yield digital (11, 89, 1070)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(2789, 1070, F27, 78) (dual of [1070, 981, 79]-code), but
- the Johnson bound shows that N ≤ 1 448630 870208 097658 140990 374874 977023 453542 715602 389146 208734 152322 310950 508306 190203 127060 493951 014795 300431 161988 014590 699883 869169 784185 466016 007918 653148 622314 329919 465085 315590 040288 331643 497653 935586 819107 612976 218097 384459 032858 985193 207094 910686 722331 113937 856683 642493 242442 275398 242169 138259 723136 719286 549833 014637 009672 013723 186029 848582 066194 880107 966097 791093 338155 236101 394328 478248 514531 566437 745716 169765 957648 374043 218350 305475 186193 607059 235460 815446 880516 812270 338322 048307 352779 846879 250321 598259 331993 845011 452496 397134 653654 827226 900049 702235 310299 396318 616437 387781 832285 676893 491443 063388 338484 902824 848199 165377 563554 568650 104847 922445 315844 591241 032860 130491 931916 657075 503091 366562 904790 291005 829768 456431 149350 872155 333256 496440 847339 132031 931964 859726 182230 739939 116541 554390 748216 528492 642381 891198 082083 866570 256096 544318 068181 013325 542559 741974 540472 600487 634082 093900 478868 598079 051257 785410 036971 582070 138552 264062 779387 150849 509938 787821 261038 684468 984880 042098 501088 519064 101669 178744 178729 230817 475719 061390 634242 746004 248378 170417 173866 313106 785257 940373 351602 187716 936073 367435 268566 561414 010917 408649 832341 866998 073520 298355 013267 210435 615838 270542 010481 942101 269426 775277 332524 913695 748112 785603 262906 626062 989638 256909 055381 367261 566529 526255 106373 983275 568672 890366 675715 316793 498249 646927 425055 425613 719774 916337 991913 057386 739669 063914 898831 782366 271100 641989 < 27981 [i]
- extracting embedded orthogonal array [i] would yield linear OA(2789, 1070, F27, 78) (dual of [1070, 981, 79]-code), but
(106−95, 106, 1073)-Net in Base 27 — Upper bound on s
There is no (11, 106, 1074)-net in base 27, because
- 15 times m-reduction [i] would yield (11, 91, 1074)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 18325 363253 897821 543890 664197 184399 064852 202259 863160 514184 120397 745019 587962 622609 674912 933576 922644 668641 664498 043491 630498 965649 > 2791 [i]