MinT - Best Known (79−65, 79, s)-Nets in Base 32

Best Known (79−65, 79, s)-Nets in Base 32

(79−65, 79, 120)-Net over F₃₂ — Constructive and digital

Digital (14, 79, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 79, 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]

(79−65, 79, 146)-Net over F₃₂ — Digital

Digital (14, 79, 146)-net over F₃₂, using

net from sequence [i] based on digital (14, 145)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 14 and N(F) ≥ 146, using
  - a curve from the manYPoints database [i]

(79−65, 79, 1908)-Net in Base 32 — Upper bound on s

There is no (14, 79, 1909)-net in base 32, because

1 times m-reduction [i] would yield (14, 78, 1909)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2563 342684 425644 205014 861895 118958 903233 491851 909535 623484 576137 863652 548648 360076 844496 318863 917632 884079 226768 001081 > 32⁷⁸ [i]