MinT - Best Known (10, 10+61, s)-Nets in Base 32

Best Known (10, 10+61, s)-Nets in Base 32

(10, 10+61, 104)-Net over F₃₂ — Constructive and digital

Digital (10, 71, 104)-net over F₃₂, using

t-expansion [i] based on digital (9, 71, 104)-net over F₃₂, using
- net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by SÃ©mirat [i]

(10, 10+61, 113)-Net over F₃₂ — Digital

Digital (10, 71, 113)-net over F₃₂, using

net from sequence [i] based on digital (10, 112)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 10 and N(F) ≥ 113, using
  - a curve from the manYPoints database [i]

(10, 10+61, 1247)-Net in Base 32 — Upper bound on s

There is no (10, 71, 1248)-net in base 32, because

1 times m-reduction [i] would yield (10, 70, 1248)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2310 428028 447521 452140 024928 345651 434581 045415 695010 458295 621280 116832 437681 281493 028729 057207 434918 748851 > 32⁷⁰ [i]