Best Known (126−93, 126, s)-Nets in Base 16
(126−93, 126, 65)-Net over F16 — Constructive and digital
Digital (33, 126, 65)-net over F16, using
- t-expansion [i] based on digital (6, 126, 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
(126−93, 126, 98)-Net in Base 16 — Constructive
(33, 126, 98)-net in base 16, using
- 4 times m-reduction [i] based on (33, 130, 98)-net in base 16, using
- base change [i] based on digital (7, 104, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- base change [i] based on digital (7, 104, 98)-net over F32, using
(126−93, 126, 193)-Net over F16 — Digital
Digital (33, 126, 193)-net over F16, using
- net from sequence [i] based on digital (33, 192)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 33 and N(F) ≥ 193, using
(126−93, 126, 2219)-Net in Base 16 — Upper bound on s
There is no (33, 126, 2220)-net in base 16, because
- 1 times m-reduction [i] would yield (33, 125, 2220)-net in base 16, but
- the generalized Rao bound for nets shows that 16m ≥ 3 311185 018575 386841 570143 353156 521442 646026 133550 921380 794254 206560 245910 547541 515201 220928 360287 653751 845454 240333 745538 463433 031186 669734 168607 126176 > 16125 [i]