Best Known (247−65, 247, s)-Nets in Base 4
(247−65, 247, 531)-Net over F4 — Constructive and digital
Digital (182, 247, 531)-net over F4, using
- t-expansion [i] based on digital (179, 247, 531)-net over F4, using
- 11 times m-reduction [i] based on digital (179, 258, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 86, 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, 86, 177)-net over F64, using
- 11 times m-reduction [i] based on digital (179, 258, 531)-net over F4, using
(247−65, 247, 648)-Net in Base 4 — Constructive
(182, 247, 648)-net in base 4, using
- 41 times duplication [i] based on (181, 246, 648)-net in base 4, using
- trace code for nets [i] based on (17, 82, 216)-net in base 64, using
- 2 times m-reduction [i] based on (17, 84, 216)-net in base 64, using
- base change [i] based on digital (5, 72, 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, 72, 216)-net over F128, using
- 2 times m-reduction [i] based on (17, 84, 216)-net in base 64, using
- trace code for nets [i] based on (17, 82, 216)-net in base 64, using
(247−65, 247, 1764)-Net over F4 — Digital
Digital (182, 247, 1764)-net over F4, using
(247−65, 247, 181147)-Net in Base 4 — Upper bound on s
There is no (182, 247, 181148)-net in base 4, because
- 1 times m-reduction [i] would yield (182, 246, 181148)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 12787 599014 200057 305573 134500 284307 316420 129489 053393 192381 379805 996611 370297 574801 939388 244016 570515 667864 386527 207426 067263 788277 034898 930288 741852 > 4246 [i]