MinT - Best Known (69−53, 69, s)-Nets in Base 32

Best Known (69−53, 69, s)-Nets in Base 32

(69−53, 69, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 69, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 69, 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]

(69−53, 69, 158)-Net over F₃₂ — Digital

Digital (16, 69, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 69, 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]

(69−53, 69, 2927)-Net in Base 32 — Upper bound on s

There is no (16, 69, 2928)-net in base 32, because

1 times m-reduction [i] would yield (16, 68, 2928)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 248563 842097 875790 813075 284436 159990 516191 442191 412456 430915 024059 012901 314108 012232 730210 120665 463306 > 32⁶⁸ [i]