Best Known (118−109, 118, s)-Nets in Base 16
(118−109, 118, 65)-Net over F16 — Constructive and digital
Digital (9, 118, 65)-net over F16, using
- t-expansion [i] based on digital (6, 118, 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
(118−109, 118, 72)-Net over F16 — Digital
Digital (9, 118, 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
(118−109, 118, 239)-Net in Base 16 — Upper bound on s
There is no (9, 118, 240)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16118, 240, S16, 109), but
- the linear programming bound shows that M ≥ 103 275542 045847 873385 157311 319616 262682 361879 592694 389449 740334 213460 696065 359862 679441 800526 188138 556540 331447 282239 220424 041878 354349 804700 586857 196947 872777 953999 218368 232200 450247 284750 485946 160707 991379 976708 651176 373865 724911 591215 857664 / 8340 776832 908360 837813 315970 683271 757878 470714 509619 634989 974373 231787 772196 098436 354327 558373 202439 > 16118 [i]