Best Known (104, 153, s)-Nets in Base 8
(104, 153, 513)-Net over F8 — Constructive and digital
Digital (104, 153, 513)-net over F8, using
- base reduction for projective spaces (embedding PG(76,64) in PG(152,8)) for nets [i] based on digital (28, 77, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(104, 153, 576)-Net in Base 8 — Constructive
(104, 153, 576)-net in base 8, using
- 13 times m-reduction [i] based on (104, 166, 576)-net in base 8, using
- trace code for nets [i] based on (21, 83, 288)-net in base 64, using
- 1 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- base change [i] based on digital (9, 72, 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, 72, 288)-net over F128, using
- 1 times m-reduction [i] based on (21, 84, 288)-net in base 64, using
- trace code for nets [i] based on (21, 83, 288)-net in base 64, using
(104, 153, 2048)-Net over F8 — Digital
Digital (104, 153, 2048)-net over F8, using
(104, 153, 734219)-Net in Base 8 — Upper bound on s
There is no (104, 153, 734220)-net in base 8, because
- 1 times m-reduction [i] would yield (104, 152, 734220)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 186075 101437 078804 361559 538296 552785 280076 051511 984919 056893 479428 054572 926623 975095 335719 988866 439997 937149 996052 599037 737795 446455 883328 > 8152 [i]