MinT - Best Known (78−61, 78, s)-Nets in Base 32

Best Known (78−61, 78, s)-Nets in Base 32

(78−61, 78, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 78, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 78, 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]

(78−61, 78, 158)-Net over F₃₂ — Digital

Digital (17, 78, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 78, 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]

(78−61, 78, 2820)-Net in Base 32 — Upper bound on s

There is no (17, 78, 2821)-net in base 32, because

1 times m-reduction [i] would yield (17, 77, 2821)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 79 513738 077809 923162 082096 022945 090633 792828 398969 622482 998236 451277 456364 826787 100763 042646 041226 462762 935079 313024 > 32⁷⁷ [i]