MinT - Best Known (70−55, 70, s)-Nets in Base 32

Best Known (70−55, 70, s)-Nets in Base 32

(70−55, 70, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 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]

(70−55, 70, 158)-Net over F₃₂ — Digital

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]

(70−55, 70, 2460)-Net in Base 32 — Upper bound on s

There is no (15, 70, 2461)-net in base 32, because

1 times m-reduction [i] would yield (15, 69, 2461)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 71 716935 395702 301052 579592 982009 351489 767030 885220 922103 746257 174636 509179 769287 514119 588793 470633 183620 > 32⁶⁹ [i]