Best Known (27, 27+50, s)-Nets in Base 128
(27, 27+50, 300)-Net over F128 — Constructive and digital
Digital (27, 77, 300)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 26, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (1, 51, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128 (see above)
- digital (1, 26, 150)-net over F128, using
(27, 27+50, 513)-Net over F128 — Digital
Digital (27, 77, 513)-net over F128, using
- t-expansion [i] based on digital (24, 77, 513)-net over F128, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 24 and N(F) ≥ 513, using
- net from sequence [i] based on digital (24, 512)-sequence over F128, using
(27, 27+50, 247746)-Net in Base 128 — Upper bound on s
There is no (27, 77, 247747)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1 799666 170461 246904 291576 046935 269578 293880 967466 951108 362654 941574 669763 608909 057949 343317 359435 948896 235872 132555 076153 354029 001290 946826 101276 816618 536140 385296 > 12877 [i]