Best Known (187−61, 187, s)-Nets in Base 4
(187−61, 187, 240)-Net over F4 — Constructive and digital
Digital (126, 187, 240)-net over F4, using
- 41 times duplication [i] based on digital (125, 186, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 62, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 62, 80)-net over F64, using
(187−61, 187, 562)-Net over F4 — Digital
Digital (126, 187, 562)-net over F4, using
(187−61, 187, 21674)-Net in Base 4 — Upper bound on s
There is no (126, 187, 21675)-net in base 4, because
- 1 times m-reduction [i] would yield (126, 186, 21675)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 9626 379813 244598 854710 445934 605646 989712 964049 866258 579531 394165 486313 546674 475815 858016 923551 993157 543371 669112 > 4186 [i]