Best Known (98−27, 98, s)-Nets in Base 4
(98−27, 98, 384)-Net over F4 — Constructive and digital
Digital (71, 98, 384)-net over F4, using
- 1 times m-reduction [i] based on digital (71, 99, 384)-net over F4, using
- trace code for nets [i] based on digital (5, 33, 128)-net over F64, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 5 and N(F) ≥ 128, using
- net from sequence [i] based on digital (5, 127)-sequence over F64, using
- trace code for nets [i] based on digital (5, 33, 128)-net over F64, using
(98−27, 98, 387)-Net in Base 4 — Constructive
(71, 98, 387)-net in base 4, using
- 1 times m-reduction [i] based on (71, 99, 387)-net in base 4, using
- trace code for nets [i] based on (5, 33, 129)-net in base 64, using
- 2 times m-reduction [i] based on (5, 35, 129)-net in base 64, using
- base change [i] based on digital (0, 30, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 30, 129)-net over F128, using
- 2 times m-reduction [i] based on (5, 35, 129)-net in base 64, using
- trace code for nets [i] based on (5, 33, 129)-net in base 64, using
(98−27, 98, 667)-Net over F4 — Digital
Digital (71, 98, 667)-net over F4, using
(98−27, 98, 58681)-Net in Base 4 — Upper bound on s
There is no (71, 98, 58682)-net in base 4, because
- 1 times m-reduction [i] would yield (71, 97, 58682)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 25110 410157 715505 077008 719476 537783 881445 582839 590985 256780 > 497 [i]