Best Known (69−37, 69, s)-Nets in Base 128
(69−37, 69, 504)-Net over F128 — Constructive and digital
Digital (32, 69, 504)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (5, 23, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- digital (9, 46, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- digital (5, 23, 216)-net over F128, using
(69−37, 69, 547)-Net in Base 128 — Constructive
(32, 69, 547)-net in base 128, using
- (u, u+v)-construction [i] based on
- (5, 23, 259)-net in base 128, using
- 1 times m-reduction [i] based on (5, 24, 259)-net in base 128, using
- base change [i] based on digital (2, 21, 259)-net over F256, using
- net from sequence [i] based on digital (2, 258)-sequence over F256, using
- base change [i] based on digital (2, 21, 259)-net over F256, using
- 1 times m-reduction [i] based on (5, 24, 259)-net in base 128, using
- digital (9, 46, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- (5, 23, 259)-net in base 128, using
(69−37, 69, 1248)-Net over F128 — Digital
Digital (32, 69, 1248)-net over F128, using
(69−37, 69, 5431210)-Net in Base 128 — Upper bound on s
There is no (32, 69, 5431211)-net in base 128, because
- 1 times m-reduction [i] would yield (32, 68, 5431211)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 195109 560151 114244 023094 215853 442236 253291 567709 938130 901838 727325 238893 749762 649513 702705 649692 486071 369393 259802 949910 544362 761395 094032 252562 > 12868 [i]