Best Known (31, 31+46, s)-Nets in Base 128
(31, 31+46, 408)-Net over F128 — Constructive and digital
Digital (31, 77, 408)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 26, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (5, 51, 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
- digital (3, 26, 192)-net over F128, using
(31, 31+46, 609)-Net over F128 — Digital
Digital (31, 77, 609)-net over F128, using
- t-expansion [i] based on digital (30, 77, 609)-net over F128, using
- net from sequence [i] based on digital (30, 608)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 30 and N(F) ≥ 609, using
- net from sequence [i] based on digital (30, 608)-sequence over F128, using
(31, 31+46, 841820)-Net in Base 128 — Upper bound on s
There is no (31, 77, 841821)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 1 799609 173659 598406 949738 631032 519052 023266 972917 456149 749773 186912 504991 442911 145083 639887 216646 693203 697780 893514 502669 824842 360217 726114 403315 744564 143004 293112 > 12877 [i]