Best Known (27, 27+39, s)-Nets in Base 3
(27, 27+39, 37)-Net over F3 — Constructive and digital
Digital (27, 66, 37)-net over F3, using
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 26, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
(27, 27+39, 39)-Net over F3 — Digital
Digital (27, 66, 39)-net over F3, using
- net from sequence [i] based on digital (27, 38)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 27 and N(F) ≥ 39, using
(27, 27+39, 147)-Net in Base 3 — Upper bound on s
There is no (27, 66, 148)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(366, 148, S3, 39), but
- the linear programming bound shows that M ≥ 12601 938564 535135 135650 704084 012491 922357 294021 765537 541685 645839 226422 815808 943462 058299 571552 747099 509046 004028 133055 653131 287247 568473 006567 967081 409762 196702 490529 324098 740118 016092 247038 547359 649040 681487 642341 125002 274190 164327 183856 840151 147540 583967 171391 388109 925272 913352 964800 / 384 059324 319862 832498 618445 532744 571583 007585 206309 391529 282484 838516 443217 531358 149541 245870 985345 825263 049658 436169 025865 545718 943340 473250 969889 220421 359249 299552 438338 207068 772943 366528 348901 499961 632144 757700 140721 271228 293983 702658 240983 860982 727927 > 366 [i]