Best Known (99−57, 99, s)-Nets in Base 32
(99−57, 99, 196)-Net over F32 — Constructive and digital
Digital (42, 99, 196)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 35, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (7, 64, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 35, 98)-net over F32, using
(99−57, 99, 288)-Net in Base 32 — Constructive
(42, 99, 288)-net in base 32, using
- t-expansion [i] based on (40, 99, 288)-net in base 32, using
- 9 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
- base change [i] based on (22, 90, 288)-net in base 64, using
- 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 78, 288)-net over F128, using
- 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
- base change [i] based on (22, 90, 288)-net in base 64, using
- 9 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
(99−57, 99, 310)-Net over F32 — Digital
Digital (42, 99, 310)-net over F32, using
(99−57, 99, 408)-Net in Base 32
(42, 99, 408)-net in base 32, using
- 3 times m-reduction [i] based on (42, 102, 408)-net in base 32, using
- base change [i] based on digital (25, 85, 408)-net over F64, using
- net from sequence [i] based on digital (25, 407)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 25 and N(F) ≥ 408, using
- net from sequence [i] based on digital (25, 407)-sequence over F64, using
- base change [i] based on digital (25, 85, 408)-net over F64, using
(99−57, 99, 67542)-Net in Base 32 — Upper bound on s
There is no (42, 99, 67543)-net in base 32, because
- 1 times m-reduction [i] would yield (42, 98, 67543)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 3197 635985 551849 532090 651071 030969 189367 695605 492690 523701 251787 627217 643635 970208 103848 919361 289997 034552 939746 426722 049609 989533 576675 192604 441464 > 3298 [i]