Best Known (35, 78, s)-Nets in Base 128
(35, 78, 504)-Net over F128 — Constructive and digital
Digital (35, 78, 504)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (5, 26, 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, 52, 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, 26, 216)-net over F128, using
(35, 78, 546)-Net in Base 128 — Constructive
(35, 78, 546)-net in base 128, using
- (u, u+v)-construction [i] based on
- (5, 26, 258)-net in base 128, using
- 6 times m-reduction [i] based on (5, 32, 258)-net in base 128, using
- base change [i] based on digital (1, 28, 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, 28, 258)-net over F256, using
- 6 times m-reduction [i] based on (5, 32, 258)-net in base 128, using
- digital (9, 52, 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, 26, 258)-net in base 128, using
(35, 78, 1086)-Net over F128 — Digital
Digital (35, 78, 1086)-net over F128, using
(35, 78, 3640191)-Net in Base 128 — Upper bound on s
There is no (35, 78, 3640192)-net in base 128, because
- 1 times m-reduction [i] would yield (35, 77, 3640192)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 1 799574 395774 990217 437655 786397 173759 436903 317640 198592 062100 200698 064671 023270 730919 378089 258532 454201 622144 812704 959625 083232 423285 361826 898432 370138 934160 089145 > 12877 [i]