Best Known (35−27, 35, s)-Nets in Base 128
(35−27, 35, 216)-Net over F128 — Constructive and digital
Digital (8, 35, 216)-net over F128, using
- t-expansion [i] based on digital (5, 35, 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
(35−27, 35, 260)-Net in Base 128 — Constructive
(8, 35, 260)-net in base 128, using
- 5 times m-reduction [i] based on (8, 40, 260)-net in base 128, using
- base change [i] based on digital (3, 35, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
- base change [i] based on digital (3, 35, 260)-net over F256, using
(35−27, 35, 276)-Net over F128 — Digital
Digital (8, 35, 276)-net over F128, using
- net from sequence [i] based on digital (8, 275)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 8 and N(F) ≥ 276, using
(35−27, 35, 321)-Net in Base 128
(8, 35, 321)-net in base 128, using
- 13 times m-reduction [i] based on (8, 48, 321)-net in base 128, using
- base change [i] based on digital (2, 42, 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, 42, 321)-net over F256, using
(35−27, 35, 14473)-Net in Base 128 — Upper bound on s
There is no (8, 35, 14474)-net in base 128, because
- 1 times m-reduction [i] would yield (8, 34, 14474)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 441772 895317 312962 290274 852681 484743 982256 057733 158155 567815 325274 517600 > 12834 [i]