Best Known (28, 28+51, s)-Nets in Base 32
(28, 28+51, 120)-Net over F32 — Constructive and digital
Digital (28, 79, 120)-net over F32, using
- t-expansion [i] based on digital (11, 79, 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
(28, 28+51, 192)-Net in Base 32 — Constructive
(28, 79, 192)-net in base 32, using
- t-expansion [i] based on (27, 79, 192)-net in base 32, using
- 5 times m-reduction [i] based on (27, 84, 192)-net in base 32, using
- base change [i] based on digital (3, 60, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- base change [i] based on digital (3, 60, 192)-net over F128, using
- 5 times m-reduction [i] based on (27, 84, 192)-net in base 32, using
(28, 28+51, 257)-Net over F32 — Digital
Digital (28, 79, 257)-net over F32, using
- net from sequence [i] based on digital (28, 256)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 28 and N(F) ≥ 257, using
(28, 28+51, 16292)-Net in Base 32 — Upper bound on s
There is no (28, 79, 16293)-net in base 32, because
- 1 times m-reduction [i] would yield (28, 78, 16293)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 2523 203463 745719 370094 424417 800492 191259 514653 417064 175487 675022 669482 856794 692958 467819 720906 875709 353001 981053 755408 > 3278 [i]