Best Known (95, 95+∞, s)-Nets in Base 7
(95, 95+∞, 76)-Net over F7 — Constructive and digital
Digital (95, m, 76)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (95, 75)-sequence over F7, using
- Niederreiter–Xing sequence construction III based on function field F2/F7 with g(F2) = 21, N(F2) ≥ 2, and N(F2) + N2(F2) ≥ 76 from GarcÃa–Stichtenoth tower as constant field extension [i]
(95, 95+∞, 105)-Net over F7 — Digital
Digital (95, m, 105)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (95, 104)-sequence over F7, using
- t-expansion [i] based on digital (43, 104)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 43 and N(F) ≥ 105, using
- t-expansion [i] based on digital (43, 104)-sequence over F7, using
(95, 95+∞, 593)-Net in Base 7 — Upper bound on s
There is no (95, m, 594)-net in base 7 for arbitrarily large m, because
- m-reduction [i] would yield (95, 1778, 594)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(71778, 594, S7, 3, 1683), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 163961 929474 413849 838355 169310 897494 223754 094081 279666 000186 698947 257850 913606 783717 723656 172128 534906 794994 905415 726473 713278 364368 198905 866184 690136 013710 658615 012146 903971 333173 137303 136338 301144 789495 666341 344065 277705 011941 717015 149071 372379 286302 945927 734740 178617 380855 351228 328526 221141 245737 361089 148350 577630 099760 343746 186894 364489 890452 725145 800104 892787 233700 207933 351706 513778 619203 548443 994491 567718 649922 604812 587752 673415 391112 932494 776255 333021 869531 863116 995862 623987 196564 689209 958532 886046 429810 317655 534933 083820 947293 773092 603478 751529 871415 519464 340324 988430 977263 829876 823207 626034 111741 901958 393986 571522 298139 443909 904949 611773 203872 575623 217284 035222 588192 685729 768545 715065 226138 936614 434482 652896 881679 717191 538199 209889 548666 850090 340566 619696 856136 827467 880689 447059 503400 739455 248553 141319 206221 463112 031098 577772 957177 580964 574908 636992 358984 661449 054264 814311 023413 247082 423262 577475 205369 650838 099293 773803 672644 042241 071679 274441 325017 260116 114463 327402 187511 151288 733620 533600 354963 590768 769300 482552 533309 064172 576300 647434 425247 158308 352475 636912 656248 041742 539910 959177 329930 575246 559637 935955 170954 943848 264529 563054 027216 741636 712915 360395 315131 041841 869295 423122 033707 816152 847502 814766 664772 054837 104107 171274 868374 799232 866487 716859 682219 383514 366846 634515 902702 945514 985358 470347 497313 332050 924617 205624 507932 443216 502095 564616 961140 361765 808133 852256 324572 542928 432517 408546 885962 148137 350597 487526 206418 470024 609162 303388 959427 541820 552899 514069 820325 649723 / 421 > 71778 [i]
- extracting embedded OOA [i] would yield OOA(71778, 594, S7, 3, 1683), but