Best Known (115−106, 115, s)-Nets in Base 16
(115−106, 115, 65)-Net over F16 — Constructive and digital
Digital (9, 115, 65)-net over F16, using
- t-expansion [i] based on digital (6, 115, 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
(115−106, 115, 72)-Net over F16 — Digital
Digital (9, 115, 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
(115−106, 115, 247)-Net in Base 16 — Upper bound on s
There is no (9, 115, 248)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16115, 248, S16, 106), but
- the linear programming bound shows that M ≥ 24130 992354 968741 564288 527488 246495 856552 035381 140063 360454 801047 899928 340573 222121 154556 178179 023713 665797 999350 304601 631294 701225 800973 105585 699130 121463 687919 181469 699246 055572 869312 931012 624164 049298 431596 433431 579854 703079 327792 001696 425635 170079 788270 354432 / 7655 835418 469638 314569 067655 783026 259377 212922 860899 885465 533696 942921 886021 725986 204812 064921 673451 918464 943433 293731 086437 > 16115 [i]