Best Known (36−23, 36, s)-Nets in Base 128
(36−23, 36, 300)-Net over F128 — Constructive and digital
Digital (13, 36, 300)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (1, 24, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128 (see above)
- digital (1, 12, 150)-net over F128, using
(36−23, 36, 321)-Net over F128 — Digital
Digital (13, 36, 321)-net over F128, using
- t-expansion [i] based on digital (12, 36, 321)-net over F128, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 12 and N(F) ≥ 321, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
(36−23, 36, 513)-Net in Base 128
(13, 36, 513)-net in base 128, using
- 4 times m-reduction [i] based on (13, 40, 513)-net in base 128, using
- base change [i] based on digital (8, 35, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- base change [i] based on digital (8, 35, 513)-net over F256, using
(36−23, 36, 195865)-Net in Base 128 — Upper bound on s
There is no (13, 36, 195866)-net in base 128, because
- 1 times m-reduction [i] would yield (13, 35, 195866)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 56 540399 222779 740414 956544 360159 233709 313242 691289 557308 182631 054658 363336 > 12835 [i]