MinT - Best Known (64−43, 64, s)-Nets in Base 32

Best Known (64−43, 64, s)-Nets in Base 32

(64−43, 64, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 64, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 64, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(64−43, 64, 177)-Net in Base 32 — Constructive

(21, 64, 177)-net in base 32, using

20 times m-reduction [i] based on (21, 84, 177)-net in base 32, using
- base change [i] based on digital (7, 70, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(64−43, 64, 185)-Net over F₃₂ — Digital

Digital (21, 64, 185)-net over F₃₂, using

net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
  - a curve from the manYPoints database [i]

(64−43, 64, 225)-Net in Base 32

(21, 64, 225)-net in base 32, using

2 times m-reduction [i] based on (21, 66, 225)-net in base 32, using
- base change [i] based on digital (10, 55, 225)-net over F₆₄, using
  - net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
      - a curve from the manYPoints database [i]

(64−43, 64, 9163)-Net in Base 32 — Upper bound on s

There is no (21, 64, 9164)-net in base 32, because

1 times m-reduction [i] would yield (21, 63, 9164)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 66781 441283 721459 933130 552769 000354 778591 217974 942441 134429 132791 035546 869056 275983 441274 031240 > 32⁶³ [i]