Best Known (38−30, 38, s)-Nets in Base 128
(38−30, 38, 216)-Net over F128 — Constructive and digital
Digital (8, 38, 216)-net over F128, using
- t-expansion [i] based on digital (5, 38, 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
(38−30, 38, 260)-Net in Base 128 — Constructive
(8, 38, 260)-net in base 128, using
- 2 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
(38−30, 38, 276)-Net over F128 — Digital
Digital (8, 38, 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
(38−30, 38, 321)-Net in Base 128
(8, 38, 321)-net in base 128, using
- 10 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
(38−30, 38, 11014)-Net in Base 128 — Upper bound on s
There is no (8, 38, 11015)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 118 722098 819191 760803 993827 572781 851593 918280 906938 559438 571378 074066 793053 982976 > 12838 [i]