Best Known (13, 94, s)-Nets in Base 27
(13, 94, 96)-Net over F27 — Constructive and digital
Digital (13, 94, 96)-net over F27, using
- t-expansion [i] based on digital (11, 94, 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
(13, 94, 136)-Net over F27 — Digital
Digital (13, 94, 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
(13, 94, 1268)-Net over F27 — Upper bound on s (digital)
There is no digital (13, 94, 1269)-net over F27, because
- 1 times m-reduction [i] would yield digital (13, 93, 1269)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(2793, 1269, F27, 80) (dual of [1269, 1176, 81]-code), but
- the Johnson bound shows that N ≤ 1873 005014 582030 642210 769528 720015 820964 881569 306785 633417 919577 216959 797172 216079 243899 617317 705079 174656 493254 928941 193943 003768 897281 737780 753517 436164 375032 135879 982583 455251 594529 880483 715222 938437 453953 811297 726260 949438 951283 011694 328070 098270 685855 250234 510410 352276 796412 439186 586907 691387 251797 703655 844991 622973 084462 352953 801347 190140 257266 605195 679511 890279 549174 332988 385282 120059 132642 585604 922895 644426 727603 201305 443803 807950 332803 124565 105052 928037 599037 108845 078659 952287 053424 781395 879461 404528 809396 753149 454606 497430 351465 717879 166725 279180 694676 633518 354147 090666 236184 939075 091618 948837 154090 481569 003166 931868 399980 447312 390906 264092 514127 930151 422542 458591 398988 394803 204003 460214 020961 303227 893170 919375 927924 983909 901295 704660 086841 001337 344700 378703 361982 707479 351511 086414 198650 640160 904707 254079 596878 281034 499790 743608 139363 450793 876590 896707 974763 712124 932791 002216 408742 548544 382650 992509 749110 104924 321402 417003 478908 083699 454045 027475 285974 834577 302853 374753 641605 041065 931188 686548 793621 299707 148367 613622 517833 269396 152674 507973 144886 181730 860207 053324 556675 268377 467742 524259 524567 888352 653818 623602 120789 947649 977495 286872 941585 148938 688466 388458 221645 689588 866127 275063 752267 715930 591006 016911 049316 540031 125352 521937 830319 143373 027511 737113 006783 302401 621191 284633 104122 800172 068007 018517 879774 339505 652051 830489 232754 132631 434236 372833 120345 748040 935147 638130 954809 028904 080787 369964 549815 818815 416329 778320 756082 442125 361860 048321 659191 042857 259649 748629 340339 553342 052126 233682 119863 066062 366055 792059 044215 516375 589951 499485 360144 057337 859217 387691 149731 306466 238099 957522 187456 425753 091898 405370 455425 158748 175153 554704 617067 187968 858419 < 271176 [i]
- extracting embedded orthogonal array [i] would yield linear OA(2793, 1269, F27, 80) (dual of [1269, 1176, 81]-code), but
(13, 94, 1269)-Net in Base 27 — Upper bound on s
There is no (13, 94, 1270)-net in base 27, because
- 1 times m-reduction [i] would yield (13, 93, 1270)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 13 299652 055979 105381 242965 857932 736915 240529 993330 924114 371304 199746 291746 032075 064204 940878 946060 548916 355531 282245 802610 259394 965521 > 2793 [i]