Best Known (21−14, 21, s)-Nets in Base 128
(21−14, 21, 258)-Net over F128 — Constructive and digital
Digital (7, 21, 258)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 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, 14, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
- digital (0, 7, 129)-net over F128, using
(21−14, 21, 261)-Net in Base 128 — Constructive
(7, 21, 261)-net in base 128, using
- 3 times m-reduction [i] based on (7, 24, 261)-net in base 128, using
- base change [i] based on digital (4, 21, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- base change [i] based on digital (4, 21, 261)-net over F256, using
(21−14, 21, 262)-Net over F128 — Digital
Digital (7, 21, 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
(21−14, 21, 321)-Net in Base 128
(7, 21, 321)-net in base 128, using
- 19 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
(21−14, 21, 55811)-Net in Base 128 — Upper bound on s
There is no (7, 21, 55812)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 178 424715 841955 600369 356034 614304 655712 327552 > 12821 [i]