Best Known (83−74, 83, s)-Nets in Base 25
(83−74, 83, 104)-Net over F25 — Constructive and digital
Digital (9, 83, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
(83−74, 83, 805)-Net over F25 — Upper bound on s (digital)
There is no digital (9, 83, 806)-net over F25, because
- 8 times m-reduction [i] would yield digital (9, 75, 806)-net over F25, but
- extracting embedded orthogonal array [i] would yield linear OA(2575, 806, F25, 66) (dual of [806, 731, 67]-code), but
- the Johnson bound shows that N ≤ 78 012968 600491 470253 039648 957303 049846 680478 980847 469853 500753 293842 279487 187793 872666 668748 072773 472731 295220 043775 799664 736658 990170 135586 897143 525869 951495 703429 774814 764103 876764 767552 387175 306055 092416 388048 022612 222964 031037 883822 201623 444277 147562 141727 323848 899910 740912 073276 746639 174184 004200 513918 733669 699720 466729 271342 203245 724793 341232 226635 614144 473750 484235 666436 661896 495396 129570 233628 683968 565857 645490 969950 267364 291567 601186 459672 416669 501150 182099 733642 794608 748972 567834 178182 933455 981529 553709 565562 236927 234147 911637 952399 130099 798783 210821 957164 412256 112271 126029 811178 533650 917593 583082 545221 081947 034293 486930 335555 463968 184433 562812 665044 211902 315039 027184 075857 912381 801662 513476 138239 139672 132038 755537 493204 547310 020231 471328 787136 599239 419223 357177 290143 745508 407357 477411 353760 990461 650465 332358 557728 409996 762258 490174 697064 489861 257533 276491 399939 194083 310294 836583 417412 604775 677912 052822 006798 598256 909436 609729 502038 483433 199177 347872 177297 641173 826547 536387 889208 922228 270205 552932 < 25731 [i]
- extracting embedded orthogonal array [i] would yield linear OA(2575, 806, F25, 66) (dual of [806, 731, 67]-code), but
(83−74, 83, 806)-Net in Base 25 — Upper bound on s
There is no (9, 83, 807)-net in base 25, because
- 10 times m-reduction [i] would yield (9, 73, 807)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 1 127559 302147 862611 214871 560818 187110 520982 799772 634391 953962 554154 098206 888833 094294 554768 527481 095425 > 2573 [i]