Best Known (33−26, 33, s)-Nets in Base 128
(33−26, 33, 216)-Net over F128 — Constructive and digital
Digital (7, 33, 216)-net over F128, using
- t-expansion [i] based on digital (5, 33, 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
(33−26, 33, 259)-Net in Base 128 — Constructive
(7, 33, 259)-net in base 128, using
- 7 times m-reduction [i] based on (7, 40, 259)-net in base 128, using
- base change [i] based on digital (2, 35, 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, 35, 259)-net over F256, using
(33−26, 33, 262)-Net over F128 — Digital
Digital (7, 33, 262)-net over F128, using
- net from sequence [i] based on digital (7, 261)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 7 and N(F) ≥ 262, using
(33−26, 33, 321)-Net in Base 128
(7, 33, 321)-net in base 128, using
- 7 times m-reduction [i] based on (7, 40, 321)-net in base 128, using
- base change [i] based on digital (2, 35, 321)-net over F256, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 2 and N(F) ≥ 321, using
- net from sequence [i] based on digital (2, 320)-sequence over F256, using
- base change [i] based on digital (2, 35, 321)-net over F256, using
(33−26, 33, 9963)-Net in Base 128 — Upper bound on s
There is no (7, 33, 9964)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 3453 525339 573172 250768 267239 320200 079673 637191 923966 048029 800243 189160 > 12833 [i]