Best Known (104−91, 104, s)-Nets in Base 27
(104−91, 104, 96)-Net over F27 — Constructive and digital
Digital (13, 104, 96)-net over F27, using
- t-expansion [i] based on digital (11, 104, 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
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
(104−91, 104, 136)-Net over F27 — Digital
Digital (13, 104, 136)-net over F27, 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
(104−91, 104, 1253)-Net over F27 — Upper bound on s (digital)
There is no digital (13, 104, 1254)-net over F27, because
- 1 times m-reduction [i] would yield digital (13, 103, 1254)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(27103, 1254, F27, 90) (dual of [1254, 1151, 91]-code), but
- the Johnson bound shows that N ≤ 3137 072402 117671 756896 078115 037129 368006 342568 289263 454946 621025 454517 145230 695259 368383 123102 879702 515835 908067 530974 822026 773758 999496 480199 817682 994696 005283 438064 318417 417952 577360 981706 588126 463001 337621 040058 980618 738380 025288 183636 597556 400245 653116 486241 483971 679129 305334 098209 818106 057906 954331 920786 401116 135038 858744 370867 426717 243323 562247 568637 437348 058472 274920 527562 351856 197033 827873 469822 626647 500058 045619 704845 573423 775181 880027 510628 874510 736699 077957 344790 554242 470221 854454 874369 412234 684907 060325 089173 273690 743150 114962 302109 818646 942246 647281 676756 144508 719321 540514 439869 183967 220022 297749 583547 167395 432457 717267 105956 064279 613018 583262 041844 143012 203676 186463 719196 617250 433005 929935 837562 161501 450390 986827 228165 709226 629236 633255 547465 279900 885729 966799 050731 846286 021180 208613 775834 915812 957707 471199 010322 070225 724735 778098 536433 622637 219356 978722 301968 915095 876730 166717 162732 454025 006091 673306 586471 962060 336007 030482 681818 285749 020448 737564 837290 367545 655899 000270 756672 803134 407161 830944 579436 281320 736163 074989 539851 352486 016860 624513 588035 203552 562778 955066 961495 182752 246901 813171 158547 917479 140836 034034 302883 720159 459005 014546 443778 805291 126879 965868 676497 322061 473933 219858 014349 632186 287021 425907 372078 384578 439229 318573 746974 013491 448206 677404 340413 017488 267297 183206 628588 677544 123836 274109 039959 367840 372434 983796 547276 472417 858738 700226 886691 013091 579408 016566 598311 285494 378962 471415 300725 414164 048266 036195 153122 735255 225766 134867 945196 326198 891995 438241 444529 981345 850129 482117 796777 639846 971492 643102 327099 598302 192291 585484 131823 138119 653090 321646 145603 925476 250654 805385 192724 344161 412974 399627 < 271151 [i]
- extracting embedded orthogonal array [i] would yield linear OA(27103, 1254, F27, 90) (dual of [1254, 1151, 91]-code), but
(104−91, 104, 1257)-Net in Base 27 — Upper bound on s
There is no (13, 104, 1258)-net in base 27, because
- 1 times m-reduction [i] would yield (13, 103, 1258)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 2788 541003 407777 103802 585051 916407 192782 516798 250868 589968 478566 832244 969724 492735 424626 830825 448703 256040 063573 076088 174646 144069 122883 524256 308621 > 27103 [i]