Best Known (98−85, 98, s)-Nets in Base 27
(98−85, 98, 96)-Net over F27 — Constructive and digital
Digital (13, 98, 96)-net over F27, using
- t-expansion [i] based on digital (11, 98, 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
(98−85, 98, 136)-Net over F27 — Digital
Digital (13, 98, 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
(98−85, 98, 1258)-Net over F27 — Upper bound on s (digital)
There is no digital (13, 98, 1259)-net over F27, because
- 1 times m-reduction [i] would yield digital (13, 97, 1259)-net over F27, but
- extracting embedded orthogonal array [i] would yield linear OA(2797, 1259, F27, 84) (dual of [1259, 1162, 85]-code), but
- the Johnson bound shows that N ≤ 17 247998 652964 460578 777794 604123 691075 709642 229649 998947 191811 862250 481519 058504 125359 189112 905367 332624 902129 540199 421946 745810 455708 636237 281790 278136 075177 402557 376616 045883 775327 088633 652135 332138 101156 488985 457542 950524 202689 877505 179569 464756 704924 383878 549961 284530 555564 684569 900027 936569 743358 936499 350197 927558 954066 330631 618283 314504 710789 564383 308187 492822 778962 136079 892376 746069 493887 149951 839229 223569 573467 262869 997877 082446 734519 105386 230229 511549 218303 032067 245593 284065 326578 482320 638569 291031 123515 390013 289102 580573 037591 171696 190141 138127 592979 061290 742987 511401 832689 655435 119194 273456 482196 654273 624349 224878 722720 369485 101679 796093 782793 501717 400777 621184 582176 415159 877361 500687 352711 524629 915577 526965 818420 495189 613143 984551 843009 614877 833794 350430 015076 593474 983212 216061 572947 587118 830722 662057 765536 726032 056114 731486 687097 169777 381799 204335 093546 237104 214137 400349 247303 384182 021545 717424 601637 737737 038374 846810 899590 554897 169466 918295 089195 501555 085019 555059 019104 397904 776817 329243 005985 755337 656931 157178 124493 479690 289343 356921 555022 254034 890260 025669 459808 480247 361588 499226 721610 925331 683391 412510 693634 130066 716605 191248 760423 673511 368784 818217 455999 402077 639497 590707 965279 180849 929572 424686 547573 875422 040552 701900 710714 360629 818024 017129 111907 876308 433754 226106 610298 706993 326947 878160 350920 069004 590522 598558 658504 658857 783028 775125 369894 286433 125454 427837 039978 101461 071682 330934 029801 200953 359134 641291 190541 520817 112842 035988 381749 028412 285091 897261 675797 942154 234698 651390 650161 210685 361071 994584 782734 826122 706632 894650 933663 455914 675544 173919 678827 034044 286620 872740 759552 501703 139904 586970 765826 146106 420240 407808 < 271162 [i]
- extracting embedded orthogonal array [i] would yield linear OA(2797, 1259, F27, 84) (dual of [1259, 1162, 85]-code), but
(98−85, 98, 1262)-Net in Base 27 — Upper bound on s
There is no (13, 98, 1263)-net in base 27, because
- 1 times m-reduction [i] would yield (13, 97, 1263)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 7 171078 651419 532265 479271 788322 947173 424661 615760 111419 306734 526186 805122 728224 093459 834158 173336 212478 731879 742996 997145 343073 760615 685533 > 2797 [i]