Best Known (103−66, 103, s)-Nets in Base 32
(103−66, 103, 120)-Net over F32 — Constructive and digital
Digital (37, 103, 120)-net over F32, using
- t-expansion [i] based on digital (11, 103, 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
(103−66, 103, 216)-Net in Base 32 — Constructive
(37, 103, 216)-net in base 32, using
- t-expansion [i] based on (36, 103, 216)-net in base 32, using
- 5 times m-reduction [i] based on (36, 108, 216)-net in base 32, using
- base change [i] based on (18, 90, 216)-net in base 64, using
- 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- base change [i] based on digital (5, 78, 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, 78, 216)-net over F128, using
- 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
- base change [i] based on (18, 90, 216)-net in base 64, using
- 5 times m-reduction [i] based on (36, 108, 216)-net in base 32, using
(103−66, 103, 273)-Net over F32 — Digital
Digital (37, 103, 273)-net over F32, using
- t-expansion [i] based on digital (30, 103, 273)-net over F32, using
- net from sequence [i] based on digital (30, 272)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 30 and N(F) ≥ 273, using
- net from sequence [i] based on digital (30, 272)-sequence over F32, using
(103−66, 103, 315)-Net in Base 32
(37, 103, 315)-net in base 32, using
- 5 times m-reduction [i] based on (37, 108, 315)-net in base 32, using
- base change [i] based on digital (19, 90, 315)-net over F64, using
- net from sequence [i] based on digital (19, 314)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 19 and N(F) ≥ 315, using
- net from sequence [i] based on digital (19, 314)-sequence over F64, using
- base change [i] based on digital (19, 90, 315)-net over F64, using
(103−66, 103, 21160)-Net in Base 32 — Upper bound on s
There is no (37, 103, 21161)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 107274 132250 121665 378096 994409 567368 199332 085938 236596 379699 439382 680600 510098 530583 610117 288883 228747 161899 367830 379364 429238 999043 233035 202293 059504 441816 > 32103 [i]