Best Known (31, 31+36, s)-Nets in Base 128
(31, 31+36, 480)-Net over F128 — Constructive and digital
Digital (31, 67, 480)-net over F128, using
- 2 times m-reduction [i] based on digital (31, 69, 480)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 22, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (9, 47, 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 (3, 22, 192)-net over F128, using
- (u, u+v)-construction [i] based on
(31, 31+36, 546)-Net in Base 128 — Constructive
(31, 67, 546)-net in base 128, using
- (u, u+v)-construction [i] based on
- (4, 22, 258)-net in base 128, using
- 2 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
- base change [i] based on digital (1, 21, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 21, 258)-net over F256, using
- 2 times m-reduction [i] based on (4, 24, 258)-net in base 128, using
- digital (9, 45, 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
- (4, 22, 258)-net in base 128, using
(31, 31+36, 1201)-Net over F128 — Digital
Digital (31, 67, 1201)-net over F128, using
(31, 31+36, 4147908)-Net in Base 128 — Upper bound on s
There is no (31, 67, 4147909)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1524 292112 319207 539447 938699 580781 878528 400154 843252 738756 264184 439633 265123 294609 161292 665080 419895 764097 013033 372523 515403 066176 184702 479160 > 12867 [i]