Best Known (11, 11+75, s)-Nets in Base 25
(11, 11+75, 126)-Net over F25 — Constructive and digital
Digital (11, 86, 126)-net over F25, using
- t-expansion [i] based on digital (10, 86, 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
(11, 11+75, 972)-Net over F25 — Upper bound on s (digital)
There is no digital (11, 86, 973)-net over F25, because
- 1 times m-reduction [i] would yield digital (11, 85, 973)-net over F25, but
- extracting embedded orthogonal array [i] would yield linear OA(2585, 973, F25, 74) (dual of [973, 888, 75]-code), but
- the Johnson bound shows that N ≤ 230206 730731 259544 462960 722065 191035 952101 878394 308821 775353 945063 239715 290386 094319 831316 556791 727191 725102 209847 650302 000724 426915 008529 474155 180081 784327 409282 128087 996643 744982 040368 362090 882008 177687 647336 632100 286482 727793 368007 954210 244917 070122 127364 262854 093498 377670 413795 002822 852505 189151 968072 201776 237132 194961 646820 421060 551515 035301 985642 835341 795816 538006 459566 666174 588414 072877 211499 041599 983166 634352 331440 410218 607853 455287 409739 475035 912391 445334 037725 026254 041468 308473 163294 970408 205235 489997 211288 796873 710515 385384 321807 007734 579002 430751 388192 190186 658711 399954 639669 283557 946216 973082 082250 837945 695178 050225 277021 864256 927983 437993 290503 911982 477145 650898 812800 180617 702558 964191 994949 811936 130379 208922 501863 978276 951517 821684 724582 473831 545385 000666 529724 057477 469174 735846 224444 702511 551226 460433 437217 732693 598609 413917 721911 297706 275222 666577 388906 165461 990677 500859 399970 453980 500874 860523 834473 011991 330142 838005 257568 651280 693713 769092 853972 794073 698413 594536 709827 251099 736202 129815 230013 284430 351485 800034 427408 216487 431244 212492 488200 532887 696765 553923 326867 333852 552216 399277 304695 597080 227375 089024 843768 668061 827498 040805 659716 628932 487574 501677 369440 549168 332598 239344 637421 588908 409674 303263 941162 < 25888 [i]
- extracting embedded orthogonal array [i] would yield linear OA(2585, 973, F25, 74) (dual of [973, 888, 75]-code), but
(11, 11+75, 974)-Net in Base 25 — Upper bound on s
There is no (11, 86, 975)-net in base 25, because
- 1 times m-reduction [i] would yield (11, 85, 975)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 69141 612203 279322 281809 429177 010215 621707 047087 334564 728531 098853 180820 984091 832033 730812 268579 644561 595198 981002 695177 > 2585 [i]