Best Known (98−84, 98, s)-Nets in Base 25
(98−84, 98, 126)-Net over F25 — Constructive and digital
Digital (14, 98, 126)-net over F25, using
- t-expansion [i] based on digital (10, 98, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(98−84, 98, 130)-Net over F25 — Digital
Digital (14, 98, 130)-net over F25, using
- net from sequence [i] based on digital (14, 129)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 14 and N(F) ≥ 130, using
(98−84, 98, 1233)-Net over F25 — Upper bound on s (digital)
There is no digital (14, 98, 1234)-net over F25, because
- extracting embedded orthogonal array [i] would yield linear OA(2598, 1234, F25, 84) (dual of [1234, 1136, 85]-code), but
- the Johnson bound shows that N ≤ 11361 279537 176864 291231 377837 579007 171626 369648 030589 578324 647621 894726 129045 590846 504952 031637 965578 658375 240833 161385 687327 755467 820013 332359 107296 109798 542140 013172 075106 656334 312731 933874 198186 931552 835448 893749 780408 797273 447870 955162 628019 125843 165919 001263 959677 147130 612560 766591 439058 643131 822130 630057 478849 753721 295432 665059 278357 141986 721966 513744 375405 400060 123986 797518 850453 877268 365624 302026 131600 219073 203650 886635 783699 258684 016297 942101 877723 932785 645652 868598 809887 393805 238148 946857 850514 847610 006073 715333 518369 543405 503036 174655 147934 635205 571109 772811 001292 152114 481709 826834 924552 024224 751129 244163 244800 684809 869148 432563 402807 738952 072499 416446 427730 380816 296145 907636 548390 039081 842367 195057 915840 599049 266666 226496 003431 554848 285243 913777 326148 252846 385469 562205 887867 229952 288055 962359 037294 730130 920925 986546 956022 730888 235778 569535 128605 071188 229953 918710 890796 293046 204356 449055 055744 672240 147669 461423 330802 831328 990065 237999 602534 453418 778268 478744 181152 560328 176455 682959 138446 391687 796398 289329 478918 061821 179473 371667 878050 890536 809649 382096 081301 915952 551609 642552 263435 184083 852336 667839 502472 767241 944684 236793 962226 244532 135964 467742 630685 300484 693587 545641 148137 027355 535026 864424 097665 698681 650045 588804 849139 121250 707290 717991 630366 281360 023245 585854 800207 671381 182154 497236 843758 803244 077949 545447 465136 006840 810752 159383 465075 796563 009395 718308 914715 377065 973762 860687 203026 048058 497581 932865 263994 421252 073944 888743 247397 144259 644818 083574 314807 126897 850740 187779 523763 619466 252880 201679 306978 262247 070420 515925 684325 825414 990216 110120 975441 < 251136 [i]
(98−84, 98, 1235)-Net in Base 25 — Upper bound on s
There is no (14, 98, 1236)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 102360 695791 109848 399661 008306 533404 864948 825479 124327 729970 341254 414245 302143 680858 571939 752236 941717 691754 838462 862666 177840 866528 559425 > 2598 [i]