Best Known (203, 203+∞, s)-Nets in Base 3
(203, 203+∞, 112)-Net over F3 — Constructive and digital
Digital (203, m, 112)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (203, 111)-sequence over F3, using
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on function field F4/F3 with g(F4) = 79, N(F4) ≥ 2, and N(F4) + N2(F4) ≥ 112 from GarcÃa–Stichtenoth tower as constant field extension [i]
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
(203, 203+∞, 163)-Net over F3 — Digital
Digital (203, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (203, 162)-sequence over F3, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 151 and N(F) ≥ 163, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
(203, 203+∞, 420)-Net in Base 3 — Upper bound on s
There is no (203, m, 421)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (203, 2519, 421)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32519, 421, S3, 6, 2316), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 195669 257553 785888 780599 353297 646341 447950 632595 915429 050763 738775 206422 147863 299755 482738 288573 582345 024543 028125 209437 359602 856000 994390 502425 643159 065044 481735 967621 735243 280530 130493 632301 631996 480150 179554 726719 814234 439197 910946 440588 438292 129394 152508 727962 005149 836818 071429 034437 360876 363812 160994 210920 007763 817050 326073 110474 712200 004114 700406 707044 493955 702580 980584 680244 509031 985132 861964 887436 031805 677181 089842 025100 595469 390143 937272 010877 097831 742500 085272 168467 129154 901409 790211 175669 828114 930424 398188 836539 267083 020168 604438 516651 495098 832959 401799 547096 679804 855146 064962 017769 519995 145214 526429 928299 058305 522613 807274 206596 851239 214577 328089 771602 877269 084529 348125 251292 566209 657558 595920 058920 952143 754903 469995 822211 177262 571380 685268 273509 227004 000988 211571 549047 826343 239710 390586 972727 309912 013974 749253 346515 234217 991890 002179 172650 554187 563157 608359 493776 565418 196533 291084 333874 448758 984929 243497 535935 744840 813279 482331 700876 229751 119523 747589 156558 006041 279088 891963 413755 469492 659517 721384 002108 599066 897691 641979 733934 655577 494897 161390 434671 874135 810490 448597 081316 734811 964909 362963 874469 381437 002486 742246 405753 169859 484563 957809 529497 265000 684939 029636 622838 776083 / 2317 > 32519 [i]
- extracting embedded OOA [i] would yield OOA(32519, 421, S3, 6, 2316), but