Best Known (259−68, 259, s)-Nets in Base 4
(259−68, 259, 536)-Net over F4 — Constructive and digital
Digital (191, 259, 536)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 34, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (157, 225, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 75, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 75, 177)-net over F64, using
- digital (0, 34, 5)-net over F4, using
(259−68, 259, 648)-Net in Base 4 — Constructive
(191, 259, 648)-net in base 4, using
- 41 times duplication [i] based on (190, 258, 648)-net in base 4, using
- trace code for nets [i] based on (18, 86, 216)-net in base 64, using
- 5 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- base change [i] based on digital (5, 78, 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
- base change [i] based on digital (5, 78, 216)-net over F128, using
- 5 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- trace code for nets [i] based on (18, 86, 216)-net in base 64, using
(259−68, 259, 1860)-Net over F4 — Digital
Digital (191, 259, 1860)-net over F4, using
(259−68, 259, 174006)-Net in Base 4 — Upper bound on s
There is no (191, 259, 174007)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 858199 166578 287988 041332 598435 587222 054046 362899 655372 515985 336384 236071 924010 072100 045212 426547 563892 173440 548239 496471 695504 759502 567398 895441 779749 909517 > 4259 [i]