Best Known (89−83, 89, s)-Nets in Base 16
(89−83, 89, 65)-Net over F16 — Constructive and digital
Digital (6, 89, 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
(89−83, 89, 164)-Net in Base 16 — Upper bound on s
There is no (6, 89, 165)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(1689, 165, S16, 83), but
- the linear programming bound shows that M ≥ 15352 684767 685611 086882 809761 984160 188561 571509 004484 738285 092713 831920 008077 971129 525920 055364 921813 182353 415776 911815 913281 106245 860502 560348 270257 729557 233664 / 103836 312412 686023 017550 716368 186316 554556 371946 618739 > 1689 [i]