MinT - Best Known (70−53, 70, s)-Nets in Base 32

Best Known (70−53, 70, s)-Nets in Base 32

(70−53, 70, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 70, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 70, 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]

(70−53, 70, 128)-Net in Base 32 — Constructive

(17, 70, 128)-net in base 32, using

2 times m-reduction [i] based on (17, 72, 128)-net in base 32, using
- base change [i] based on digital (5, 60, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(70−53, 70, 158)-Net over F₃₂ — Digital

Digital (17, 70, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 70, 158)-net over F₃₂, using
- net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
    - an algebraic function field by Beelen and Pellikaan [i]

(70−53, 70, 3346)-Net in Base 32 — Upper bound on s

There is no (17, 70, 3347)-net in base 32, because

1 times m-reduction [i] would yield (17, 69, 3347)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 71 730774 536793 283053 868035 048788 389414 633288 587895 275894 262332 899215 073635 099052 937411 199449 849612 315680 > 32⁶⁹ [i]