Best Known (106−97, 106, s)-Nets in Base 16
(106−97, 106, 65)-Net over F16 — Constructive and digital
Digital (9, 106, 65)-net over F16, using
- t-expansion [i] based on digital (6, 106, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(106−97, 106, 72)-Net over F16 — Digital
Digital (9, 106, 72)-net over F16, using
- net from sequence [i] based on digital (9, 71)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 9 and N(F) ≥ 72, using
(106−97, 106, 294)-Net in Base 16 — Upper bound on s
There is no (9, 106, 295)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16106, 295, S16, 97), but
- the linear programming bound shows that M ≥ 31244 013797 192015 681967 395597 437107 529270 615524 637018 467023 589160 731803 956926 759215 629970 958919 023983 210861 873467 483086 921360 648696 561173 086864 471136 497238 745693 389127 105929 523362 279734 591422 669570 371023 085109 055062 016000 / 697 585023 311285 692536 118760 448527 983595 588498 371769 184971 387632 052091 656542 271487 094568 488261 > 16106 [i]