Best Known (54−46, 54, s)-Nets in Base 128
(54−46, 54, 216)-Net over F128 — Constructive and digital
Digital (8, 54, 216)-net over F128, using
- t-expansion [i] based on digital (5, 54, 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
(54−46, 54, 258)-Net in Base 128 — Constructive
(8, 54, 258)-net in base 128, using
- 2 times m-reduction [i] based on (8, 56, 258)-net in base 128, using
- base change [i] based on digital (1, 49, 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, 49, 258)-net over F256, using
(54−46, 54, 276)-Net over F128 — Digital
Digital (8, 54, 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
(54−46, 54, 289)-Net in Base 128
(8, 54, 289)-net in base 128, using
- 2 times m-reduction [i] based on (8, 56, 289)-net in base 128, using
- base change [i] based on digital (1, 49, 289)-net over F256, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- base change [i] based on digital (1, 49, 289)-net over F256, using
(54−46, 54, 6565)-Net in Base 128 — Upper bound on s
There is no (8, 54, 6566)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 616454 486163 911206 082287 788210 630805 735706 300955 891096 155764 847993 889812 687120 256400 629955 852350 188462 433831 173616 > 12854 [i]