Best Known (20−14, 20, s)-Nets in Base 128
(20−14, 20, 216)-Net over F128 — Constructive and digital
Digital (6, 20, 216)-net over F128, using
- t-expansion [i] based on digital (5, 20, 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
(20−14, 20, 243)-Net over F128 — Digital
Digital (6, 20, 243)-net over F128, using
- net from sequence [i] based on digital (6, 242)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 6 and N(F) ≥ 243, using
(20−14, 20, 260)-Net in Base 128 — Constructive
(6, 20, 260)-net in base 128, using
- 4 times m-reduction [i] based on (6, 24, 260)-net in base 128, using
- base change [i] based on digital (3, 21, 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, 21, 260)-net over F256, using
(20−14, 20, 321)-Net in Base 128
(6, 20, 321)-net in base 128, using
- 12 times m-reduction [i] based on (6, 32, 321)-net in base 128, using
- base change [i] based on digital (2, 28, 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, 28, 321)-net over F256, using
(20−14, 20, 27904)-Net in Base 128 — Upper bound on s
There is no (6, 20, 27905)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1 394127 538623 286380 239533 010136 963348 043008 > 12820 [i]