Best Known (9, 9+99, s)-Nets in Base 16
(9, 9+99, 65)-Net over F16 — Constructive and digital
Digital (9, 108, 65)-net over F16, using
- t-expansion [i] based on digital (6, 108, 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
(9, 9+99, 72)-Net over F16 — Digital
Digital (9, 108, 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
(9, 9+99, 276)-Net in Base 16 — Upper bound on s
There is no (9, 108, 277)-net in base 16, because
- extracting embedded orthogonal array [i] would yield OA(16108, 277, S16, 99), but
- the linear programming bound shows that M ≥ 124 444018 874901 149253 349730 632456 739690 434006 179541 033495 098141 656787 141334 764206 546635 513877 029356 690202 352340 059349 901778 353944 473390 121091 258905 169339 193443 900346 190450 869603 398459 981871 083777 426780 546888 303175 470910 432669 470583 966826 233856 / 10971 243576 989075 796472 406111 791518 859393 820057 240451 427580 470178 600748 851394 917879 823022 516554 987781 334334 605101 > 16108 [i]