Best Known (43, 43+51, s)-Nets in Base 32
(43, 43+51, 218)-Net over F32 — Constructive and digital
Digital (43, 94, 218)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 32, 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 (11, 62, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (7, 32, 98)-net over F32, using
(43, 43+51, 288)-Net in Base 32 — Constructive
(43, 94, 288)-net in base 32, using
- t-expansion [i] based on (40, 94, 288)-net in base 32, using
- 14 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
- 14 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
(43, 43+51, 423)-Net over F32 — Digital
Digital (43, 94, 423)-net over F32, using
(43, 43+51, 425)-Net in Base 32
(43, 94, 425)-net in base 32, using
- 8 times m-reduction [i] based on (43, 102, 425)-net in base 32, using
- base change [i] based on digital (26, 85, 425)-net over F64, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 26 and N(F) ≥ 425, using
- net from sequence [i] based on digital (26, 424)-sequence over F64, using
- base change [i] based on digital (26, 85, 425)-net over F64, using
(43, 43+51, 130430)-Net in Base 32 — Upper bound on s
There is no (43, 94, 130431)-net in base 32, because
- 1 times m-reduction [i] would yield (43, 93, 130431)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 95 275936 937173 175191 221075 278350 897337 943649 903328 151785 435540 420404 497398 682687 639218 965496 830637 918070 355307 472606 239483 825124 246260 771914 > 3293 [i]