Best Known (36−20, 36, s)-Nets in Base 128
(36−20, 36, 387)-Net over F128 — Constructive and digital
Digital (16, 36, 387)-net over F128, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 6, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (0, 10, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
- digital (0, 20, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
- digital (0, 6, 129)-net over F128, using
(36−20, 36, 515)-Net in Base 128 — Constructive
(16, 36, 515)-net in base 128, using
- (u, u+v)-construction [i] based on
- (2, 12, 257)-net in base 128, using
- 4 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
- base change [i] based on digital (0, 14, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 14, 257)-net over F256, using
- 4 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
- (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, 12, 257)-net in base 128, using
(36−20, 36, 623)-Net over F128 — Digital
Digital (16, 36, 623)-net over F128, using
(36−20, 36, 1374443)-Net in Base 128 — Upper bound on s
There is no (16, 36, 1374444)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 7237 009488 343931 483186 228108 218491 851585 340576 184839 203309 316830 092711 966967 > 12836 [i]